Have you played The Last of Us? Definitely a great PS3 game, came out quite a long time ago too, should be pretty cheap on the PS3.
Terrible, just terrible.
RPG, adventure, FPS (if it isn't too generic). Only PS3 at the moment, plus my PC.
Have you played Kingdoms of Amalur: Reckoning? I've heard good things about it, but I've never played it myself. The sequels to Final Fantasy XIII are supposedly a lot better than the original, but I haven't played those either after the disaster that was FF13. There are several Dynasty Warriors games on Ps3 that are good for mindless fun, but if you're looking for anything deeper than that then avoid them. Ni No Kuni is a decent JRPG, but kind of childish and has very little challenge.
For shooters, Unreal Tournament for Ps3 is the best thing since Unreal 99... but I would just recommend playing Unreal 99 on PC instead.
Generic answer would be: Uncharted, CoD Modarn Ware, GTAV, Destiny, Far Cry 4
Ps3 really doesn't have many good games. Get a Wii U or a 3DS.