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.
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.
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)