The psychic's quite a new class, so it doesn't necessarily have all the spells. Notably they didn't include any of the player's companions in the original spell list, so their selection is comparatively limited, but this will change with time. I might have overlooked some spells, but just keep these in mind.
If you are unaware, Psychic magic doesn't use verbal or somatic components. Instead, they use thought and emotion components. Yes, this means all their spells are stilled and silenced. However, they're subject to some limitations as well. Emotion components require a certain emotion to work, and so any emotion or fear effect makes it impossible for a psychic to cast. Thought components require exquisite concentration, and so the DCs of any concentration check with a thought component increase by 10 unless you also spend a move action to centre yourself.
Another nifty thing is that they have something called undercasting: If you know a higher level version of a spell, you can cast any of the lower level version. As an example, if you know Mind Thrust IV, you also know mind thrust I, II and III. They should have made this a thing ages ago. Simply because all psychic casters are spontaneous, I'm including all of these spells in the list of good spells because they are basically a big bunch of spells. Why take one spell when you could have 4?
Also, some spells turn up sooner for Psychics than other classes, so I'm noting those in particular as nice spells since you can rub them in your Wizard's face.
Regardless of what you're looking for, most spells require either a will or a fort save, so keep that in mind as you pick spells.
0th level spells
Detect Magic: It's a magic based game, so being able to detect it is practically necessary
Detect Psychic Significant: Also called detect important plot item. Or at least, interesting item.
Light: Functionally practical. Although, you're a psychic, so holding a torch isn't so much of an issue.
Prestigiditation: Does all the tiny things like cleaning
Telekinetic Projectile: It's a nifty damage spell for the low levels when you run out of real spells (everything's about as easy to hit normally as touch at this stage, so why not?)
1st level spells
Burst of Adrenaline: Immediate action +8 to a physical stat on a single roll. Immediate actions are nice.
Burst of insight: As Burst of Adrenaline, but mental stats. Nice for will saves on things like, say, dominate person.
Shield: Nifty defense spell that stays relevant at higher levels
Mind Thrust I: The beginning of the mind thrust series. Untyped damage spell, will halves. Damage dice increase to be quite large, and begins including fatiguing and exhausting effects.
Magic Missile: Automatic force damage (so it hits basically everything)
Detect Thoughts: This is a 2nd level spell. For you, 1st. Read minds.
Silent Image: Basic multipurpose illusions. Even if you don't concentrate, it's still useful since it can stop attacks, if nothing else.
2nd level spells:
False Life: Long lasting bonus hp
Hold Person: Paralyse a humanoid. Very nice as a 2nd level spell
Hypercognition: Perform knowledge checks quickly with a large bonus. 4th level for sorcerer/wizard, but 2nd for you. Revel in it :P
Id Insinuation I: Beginning of the Id Insinuation series. Single target confusion for as long as you concentrate, plus one round. Confusion effect gets worse (roll twice and take a result of your choice) and hits more creatures with higher level versions
Mental Block: Target creature loses all abilities. Skill ranks, spells, activated feats and extraordinary, supernatural and spell-like abilities. Sort of like hold person, but hits anything
Mental Barrier I: Start of the Mental Barrier series. Immediate action shield bonus for 1 round plus extra defence vs Mind Thrusts. Shield bonus gets larger with better versions, and begins providing protection from sneak attacks and critical hits
Mirror image: Effectively immunity to physical attacks for a while. You should keep this up as often as possible.
Suggestion: This is a top 3rd level Sorcerer/wizard spell, and you get it early! Take a target out of the fight for good.
Thought Shield I: Start of the Thought Shield series. Immediate Action bonus to will saves vs mind-affecting and immunity to thought reading. Later versions improve the bonus, stun people reading your thoughts, grant extra protection vs the nasty Psychic Crush spells and ultimately lasts for rounds per level.
Status: An excuse for meta-gaming. Long lasting, long range information about multiple target's conditions.
Piercing Shriek: Single target slow, but fort negates. 2nd level bard only spell previously.
3rd level spells
Analyse Aura: Multi-purpose divination. Learn a creature's moods, health and resource pool status (such as ki), Magical effects and Alignment.
Babble: Sort of equivalent to stinking cloud, but will based. Nauseate a creature, and nearby creatures need to save or become fascinated
Borrow Fortune: Immediate action reroll, at the cost of bad luck for the next 2 rounds. It's still great utility out of combat or in a very tight spot.
Dispel Magic: Make other people's pesky magic go away
Ego Whip I: Start of the Ego Whip series. Penalty to Int, Wis or Cha, and also staggered. Later versions increase the penalty (to a maximum of -10) and increase the stagger duration (to a maximum of 1d10)
Excruciating Deformation: Long lasting damage. Saves only remove the effect for one round.
Haste: Got martial friends? They'll love you
Heroism: +2 to a lot of things. Ideally everyone has this on all the time
Telekinetic Manoeuvre: All the best bits of telekinesis (i.e. Combat Manoeuvres), 2 levels early (note that other classes get this a level later)
Synaptic Pulse: Panic Button. Stuns everything near you for a round.
4th level spells
Charm Monster: Make anything your friend for several days
Confusion: Make a big bunch of things attack each other/probably useless
Dimension Door: Teleport a short distance
Deathless: Become immune to death by hp damage (although not necessarily conscious)
Fear: Make everyone run away
Intellect Fortress I: Start of the Intellect Fortress series. Immediate action suppression of fear and emotion effects in the area (which is great since you often have emotion components and can then proceed to remove it). Advanced versions halve damage from mind-affecting damage spells and turn save partial to save negates. Honestly mostly good because of undercasting.
Mindwipe: Gives 2 negative levels and drops spell-casting abilities a lot
Telekinesis: Nice multi-purpose spell that you get a level earlier than everyone else
Telepathic Bond: Communicate Telepathically with other creatures. Nice because you get it a level early (again)
5th level spells
Explode Head: Okay, so it's not great, but it's fun. Kill a creature with fewer than 20 hp with no save, or else deal damage (fort negates). Also, you get it a level earlier than other people :P
Dominate Person: Fully control someone
Echolocation: Get blindsight, basically negating illusions and illusory defenses
Feeblemind: Make most casters useless forever
Id Insinuation V: End of the series, so nab it to get all the previous versions!
Modify Memory: A personal favourite. Does what it says on the can.
Permanency: Make some spells permanent
Psychic Asylum: Swift action spell that allows you to go back and re-read things or wait out the duration of mind-affecting effects.
Psychic Crush I: Start of the Psychic Crush series. Okay, so it's like Phantasmal killer with its 2 saves. But at least you definitely sicken something, and they don't die if they fail both, which is quite arguably better.
Song of Discord: As confusion, but particularly deadly
Synapse Overload: Guaranteed damage!? Save to avoid a long stagger
Tower of Iron Will I: This is almost terrible, except for the undercasting thing. Gain nice SR as an immediate action... but only vs psychic spells and mind-affecting effects. Lasts a round, and upgraded versions last another round.
Spell Resistance: Gain SR 12 + level. Nyah, sorcerers/wizards don't get it :P
6th level spells
Contingency: When a trigger condition occurs, a spell goes off
Disintegrate: Deal massive damage
Death Pact: Like dominate person, but you can deal actually quite a lot of damage with it if your slave is discovered.
Greater Dispel Magic: Like Dispel Magic. But Greater.
Mind Thrust VI: The last in the mind thrust series. Nab it to get all the earlier ones! Lots of damage, exhausts and stuns.
Thought Shield V: The last in the Thought Shield series. Nab it to get all the earlier ones! Big will save bonuses and lasts for rounds
Planar Binding: Have an outsider pet (terms and conditions apply)
Greater Object Possession: Unlike previous ones, this has a long enough distance and duration that you can just hide a little way away and be a chair without having your body killed or something awkward like that.
Mental Barrier V: Last in the Mental Barrier Series. Nab it to get all the earlier ones! It gives +8 shield bonus to AC and a 50% chance to negate sneak attacks/criticals.
Intellect Fortress III: Last in the Intellect Fortress series. Nab it to get all the earlier ones! That said, it's not very good for any other reason.
7th level spells
Limited Wish: Does nearly anything you want.
Waves of exhaustion: Make martials useless with no save
Spell Turning: Bounce spells back at their caster
Mind Blank: Immunity to effects that find out more information about you and +8 resistance bonus vs mind-affecting effects. It's 8th level for everyone else :P
Unshakable Zeal: Very long lasting effect that gives bonuses when you retry failed tasks
Ego Whip V: The final spell in the Ego Whip series. Nab it to get all the previous ones in the series! It now gives a -10 penalty to a mental stat and staggers for 1d10 rounds
Project Image: Cast spells from a different point
8th level spells
Bilocation: Duplicate yourself. You share all the same resources, items and actions.
Brilliant Inspiration: Reroll all attack rolls, ability checks and skill checks and take the best.
Demand: Suggestion with infinite range
Fool's Forbiddance: Creatures in the area make a will save or be confused while you concentrate. Success makes it staggered. Shame it's concentration...
Prismatic Wall: Potent defensive spell that is both challenging to remove and requires 7 consecutive saves to pass through safely.
9th level spells
Akashic Form: (nearly) Immediately revive to full hp upon death
Divide Mind: Roll twice on intelligence checks, intelligence based skill checks and will saving throws. Also perform any purely mental standard or move action as a swift action (such as cast psychic spells no more than 5th level...)
Microcosm: Permanently render a bunch of creatures comatose
Major Mind Swap: Permanently swap bodies with another creature (of the same race)
Psychic Crush V: Final spell in the Psychic Crush series. Nab it to get all the prior ones! At this point, creatures below half their hp no longer get a fortitude save and take a -2 to the will save. Makes a decent finisher.
Disjunction: Shred magic.
Wish: Does basically everything
Tower of Iron Will V: Final spell in the Tower of Iron Will series. Grab this to get all the rest! Immediate action SR 28 vs psychic spells and mind-affecting to anything nearby for several rounds.
Telekinetic Storm: Massive area damage centred on self as a panic button that also stuns creatures (but ignores friends)
Time Stop: Just what it says on the can
There's a decent chance I've missed things or included maybe not the best spells, but I think this is a pretty decent list. I've also noticed that some spells on here... aren't on the sorcerer/wizard list, even though they should be. Seems the guy running the d20pfsrd has been pretty lazy in updating things after Occult. It's worth cross referencing the Top Sorcerer/Wizard Spells as well since I didn't necessarily include everything that's good (because I missed it or maybe changed my mind)
If you are unaware, Psychic magic doesn't use verbal or somatic components. Instead, they use thought and emotion components. Yes, this means all their spells are stilled and silenced. However, they're subject to some limitations as well. Emotion components require a certain emotion to work, and so any emotion or fear effect makes it impossible for a psychic to cast. Thought components require exquisite concentration, and so the DCs of any concentration check with a thought component increase by 10 unless you also spend a move action to centre yourself.
Another nifty thing is that they have something called undercasting: If you know a higher level version of a spell, you can cast any of the lower level version. As an example, if you know Mind Thrust IV, you also know mind thrust I, II and III. They should have made this a thing ages ago. Simply because all psychic casters are spontaneous, I'm including all of these spells in the list of good spells because they are basically a big bunch of spells. Why take one spell when you could have 4?
Also, some spells turn up sooner for Psychics than other classes, so I'm noting those in particular as nice spells since you can rub them in your Wizard's face.
Regardless of what you're looking for, most spells require either a will or a fort save, so keep that in mind as you pick spells.
0th level spells
Detect Magic: It's a magic based game, so being able to detect it is practically necessary
Detect Psychic Significant: Also called detect important plot item. Or at least, interesting item.
Light: Functionally practical. Although, you're a psychic, so holding a torch isn't so much of an issue.
Prestigiditation: Does all the tiny things like cleaning
Telekinetic Projectile: It's a nifty damage spell for the low levels when you run out of real spells (everything's about as easy to hit normally as touch at this stage, so why not?)
1st level spells
Burst of Adrenaline: Immediate action +8 to a physical stat on a single roll. Immediate actions are nice.
Burst of insight: As Burst of Adrenaline, but mental stats. Nice for will saves on things like, say, dominate person.
Shield: Nifty defense spell that stays relevant at higher levels
Mind Thrust I: The beginning of the mind thrust series. Untyped damage spell, will halves. Damage dice increase to be quite large, and begins including fatiguing and exhausting effects.
Magic Missile: Automatic force damage (so it hits basically everything)
Detect Thoughts: This is a 2nd level spell. For you, 1st. Read minds.
Silent Image: Basic multipurpose illusions. Even if you don't concentrate, it's still useful since it can stop attacks, if nothing else.
2nd level spells:
False Life: Long lasting bonus hp
Hold Person: Paralyse a humanoid. Very nice as a 2nd level spell
Hypercognition: Perform knowledge checks quickly with a large bonus. 4th level for sorcerer/wizard, but 2nd for you. Revel in it :P
Id Insinuation I: Beginning of the Id Insinuation series. Single target confusion for as long as you concentrate, plus one round. Confusion effect gets worse (roll twice and take a result of your choice) and hits more creatures with higher level versions
Mental Block: Target creature loses all abilities. Skill ranks, spells, activated feats and extraordinary, supernatural and spell-like abilities. Sort of like hold person, but hits anything
Mental Barrier I: Start of the Mental Barrier series. Immediate action shield bonus for 1 round plus extra defence vs Mind Thrusts. Shield bonus gets larger with better versions, and begins providing protection from sneak attacks and critical hits
Mirror image: Effectively immunity to physical attacks for a while. You should keep this up as often as possible.
Suggestion: This is a top 3rd level Sorcerer/wizard spell, and you get it early! Take a target out of the fight for good.
Thought Shield I: Start of the Thought Shield series. Immediate Action bonus to will saves vs mind-affecting and immunity to thought reading. Later versions improve the bonus, stun people reading your thoughts, grant extra protection vs the nasty Psychic Crush spells and ultimately lasts for rounds per level.
Status: An excuse for meta-gaming. Long lasting, long range information about multiple target's conditions.
Piercing Shriek: Single target slow, but fort negates. 2nd level bard only spell previously.
3rd level spells
Analyse Aura: Multi-purpose divination. Learn a creature's moods, health and resource pool status (such as ki), Magical effects and Alignment.
Babble: Sort of equivalent to stinking cloud, but will based. Nauseate a creature, and nearby creatures need to save or become fascinated
Borrow Fortune: Immediate action reroll, at the cost of bad luck for the next 2 rounds. It's still great utility out of combat or in a very tight spot.
Dispel Magic: Make other people's pesky magic go away
Ego Whip I: Start of the Ego Whip series. Penalty to Int, Wis or Cha, and also staggered. Later versions increase the penalty (to a maximum of -10) and increase the stagger duration (to a maximum of 1d10)
Excruciating Deformation: Long lasting damage. Saves only remove the effect for one round.
Haste: Got martial friends? They'll love you
Heroism: +2 to a lot of things. Ideally everyone has this on all the time
Telekinetic Manoeuvre: All the best bits of telekinesis (i.e. Combat Manoeuvres), 2 levels early (note that other classes get this a level later)
Synaptic Pulse: Panic Button. Stuns everything near you for a round.
4th level spells
Charm Monster: Make anything your friend for several days
Confusion: Make a big bunch of things attack each other/probably useless
Dimension Door: Teleport a short distance
Deathless: Become immune to death by hp damage (although not necessarily conscious)
Fear: Make everyone run away
Intellect Fortress I: Start of the Intellect Fortress series. Immediate action suppression of fear and emotion effects in the area (which is great since you often have emotion components and can then proceed to remove it). Advanced versions halve damage from mind-affecting damage spells and turn save partial to save negates. Honestly mostly good because of undercasting.
Mindwipe: Gives 2 negative levels and drops spell-casting abilities a lot
Telekinesis: Nice multi-purpose spell that you get a level earlier than everyone else
Telepathic Bond: Communicate Telepathically with other creatures. Nice because you get it a level early (again)
5th level spells
Explode Head: Okay, so it's not great, but it's fun. Kill a creature with fewer than 20 hp with no save, or else deal damage (fort negates). Also, you get it a level earlier than other people :P
Dominate Person: Fully control someone
Echolocation: Get blindsight, basically negating illusions and illusory defenses
Feeblemind: Make most casters useless forever
Id Insinuation V: End of the series, so nab it to get all the previous versions!
Modify Memory: A personal favourite. Does what it says on the can.
Permanency: Make some spells permanent
Psychic Asylum: Swift action spell that allows you to go back and re-read things or wait out the duration of mind-affecting effects.
Psychic Crush I: Start of the Psychic Crush series. Okay, so it's like Phantasmal killer with its 2 saves. But at least you definitely sicken something, and they don't die if they fail both, which is quite arguably better.
Song of Discord: As confusion, but particularly deadly
Synapse Overload: Guaranteed damage!? Save to avoid a long stagger
Tower of Iron Will I: This is almost terrible, except for the undercasting thing. Gain nice SR as an immediate action... but only vs psychic spells and mind-affecting effects. Lasts a round, and upgraded versions last another round.
Spell Resistance: Gain SR 12 + level. Nyah, sorcerers/wizards don't get it :P
6th level spells
Contingency: When a trigger condition occurs, a spell goes off
Disintegrate: Deal massive damage
Death Pact: Like dominate person, but you can deal actually quite a lot of damage with it if your slave is discovered.
Greater Dispel Magic: Like Dispel Magic. But Greater.
Mind Thrust VI: The last in the mind thrust series. Nab it to get all the earlier ones! Lots of damage, exhausts and stuns.
Thought Shield V: The last in the Thought Shield series. Nab it to get all the earlier ones! Big will save bonuses and lasts for rounds
Planar Binding: Have an outsider pet (terms and conditions apply)
Greater Object Possession: Unlike previous ones, this has a long enough distance and duration that you can just hide a little way away and be a chair without having your body killed or something awkward like that.
Mental Barrier V: Last in the Mental Barrier Series. Nab it to get all the earlier ones! It gives +8 shield bonus to AC and a 50% chance to negate sneak attacks/criticals.
Intellect Fortress III: Last in the Intellect Fortress series. Nab it to get all the earlier ones! That said, it's not very good for any other reason.
7th level spells
Limited Wish: Does nearly anything you want.
Waves of exhaustion: Make martials useless with no save
Spell Turning: Bounce spells back at their caster
Mind Blank: Immunity to effects that find out more information about you and +8 resistance bonus vs mind-affecting effects. It's 8th level for everyone else :P
Unshakable Zeal: Very long lasting effect that gives bonuses when you retry failed tasks
Ego Whip V: The final spell in the Ego Whip series. Nab it to get all the previous ones in the series! It now gives a -10 penalty to a mental stat and staggers for 1d10 rounds
Project Image: Cast spells from a different point
8th level spells
Bilocation: Duplicate yourself. You share all the same resources, items and actions.
Brilliant Inspiration: Reroll all attack rolls, ability checks and skill checks and take the best.
Demand: Suggestion with infinite range
Fool's Forbiddance: Creatures in the area make a will save or be confused while you concentrate. Success makes it staggered. Shame it's concentration...
Prismatic Wall: Potent defensive spell that is both challenging to remove and requires 7 consecutive saves to pass through safely.
9th level spells
Akashic Form: (nearly) Immediately revive to full hp upon death
Divide Mind: Roll twice on intelligence checks, intelligence based skill checks and will saving throws. Also perform any purely mental standard or move action as a swift action (such as cast psychic spells no more than 5th level...)
Microcosm: Permanently render a bunch of creatures comatose
Major Mind Swap: Permanently swap bodies with another creature (of the same race)
Psychic Crush V: Final spell in the Psychic Crush series. Nab it to get all the prior ones! At this point, creatures below half their hp no longer get a fortitude save and take a -2 to the will save. Makes a decent finisher.
Disjunction: Shred magic.
Wish: Does basically everything
Tower of Iron Will V: Final spell in the Tower of Iron Will series. Grab this to get all the rest! Immediate action SR 28 vs psychic spells and mind-affecting to anything nearby for several rounds.
Telekinetic Storm: Massive area damage centred on self as a panic button that also stuns creatures (but ignores friends)
Time Stop: Just what it says on the can
There's a decent chance I've missed things or included maybe not the best spells, but I think this is a pretty decent list. I've also noticed that some spells on here... aren't on the sorcerer/wizard list, even though they should be. Seems the guy running the d20pfsrd has been pretty lazy in updating things after Occult. It's worth cross referencing the Top Sorcerer/Wizard Spells as well since I didn't necessarily include everything that's good (because I missed it or maybe changed my mind)