Persona 2 Eternal Punishment (look for the English translation of the psp version) (IS and EP are 2 parts of the same story you have you play them in that order)
Persona 3 Portable (p3p is more beginner friendly then p2 but imo the p2 duology is better)
God of War (chains of Olympus and ghost of Sparta)
The first one if you really love some jank in your third person ARPG games and are a bit of a(huge) masochist. The second game is the real must have imo, a lot less jank but I'd still recommend being a bit of a masochist or at least enjoy fast "stamina" based action combat like FromSoft titles.
No idea how well the controls will work, so faster-paced games like Star Wars Battlefront might be out the window. I got a lot of mileage out of Jeanne D'Arc back in the day with my PSP. It's a fun JRPG tactics game, à la Final Fantasy Tactics.
I already downloaded it, but it’s way too late at night and I read the title as “PPSSPP has been removed from the iOS App Store” and I was about to freak out