if you read a review and it mentions load times being trash, overclock and running them off a memory card fixes that 9/10 times.
also remember it plays literally every PS1 game no problem.
also if you get your Vita all hacked up, grab the "Adrenaline" homebrew which just turns it into a PSP with slightly worse battery life and like 99% compatibility.

RPG's and stuff #

• Trails FC/SC/Third (Cannot overstate how good these are. Third is only on Vita/PC, but the story is wrapped up in SC, it just adds extra background stuff)
• Trails Zero/Ao (JP - beta fan tl, probably best to play on PC)
• Nayuta no Kiseki (fan tl, ARPG. Technically a Trails game but has literally 0 to do with the rest of the series, stands alone just fine)
• 7th Dragon 2020 (fan tl)
• Ys 1/2 Chronicles, Ys: The Oath in Felghana, Ys : The Ark of Napishtim, Ys SEVEN (ARPG's)
• Disgaea 1/2
• Gurumin : A monstrous Adventure (cute!)
• Fate/Extra (maybe wait for the new version)
• Star Ocean 1 / 2
• Brave Story : New Traveller (Not amazing but it's like 60mb so fits on small memory cards no problem. oh and it's full of catgirls, so it has that going for it)
• Lunar : Silver Star Harmony
• Final Fantasy IV (Actually the best version, has every expansion built in)
• Mana Khemia (I thought it was good!)
• Persona 1 / 2:Innocent Sin / 3 (2:Eternal Punishment on PS1 is after 2 on PSP, it's a sequel!)

VN's #

• Never7 / Ever17 / Remember11 (fantl's)
• Disgaea Infinite (play Disgaea 1 first)
• Corpse Party
• Little Busters
• AIR (fantl)
• honestly the PSP is a bit of wasteland if you're into english TL'd visual novels, the Vita is better for that tbh
• think I played Tsukihime on a PSP too, but that might have been a fan port
• wait holy crap check this out; https://cdromance.com/english-patched/?search=&platform=psp

anime tie-ins that are actually good; #

• Initial D Street Stage (jp, Racer)
• Mahou Shoujo Lyrical Nanoha A's portable: The battle of the Aces: Gears of Destiny (fantl, Fighter, GOD plays better than BOA, just play GOD if you're not in it for the story)
• Sora no woto (fan tl, VN, haven't played myself, hear good things about it)
• Oreimo (fan tl, lol)
• Black Rock Shooter (no continuity with the show or OVA, edgy)
• Idolmaster SP
• Madoka Magica Portable (unfinished fan tl)

Other stuff #

• Metal Gear Solid Portable ops / Peace Walker (I ain't into this series but had fun with these two, especially PW)
• Outrun 2006 (perhaps the comfiest racing game ever? maybe!)
• Darius Burst
• me and my katamari
• Ape Escape
• Crazy Taxi (put original soundtrack mp3's in /psp/music folder and enable custom soundtrack from menu)
• i can't fucking believe they put a Miami Vice game on this, and it's good!
• Lumines
• Locoroco
• this puyo puyo thing seems good
• Super Monkey Ball
• Space Invaders Extreme
• God of War
• Ultimate Ghosts 'n Goblins
• Kenka Bancho Badass Rumble (Yakuza-lite but with delinquents, pretty good!)
• Castlevania : Dracula X