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PSP 3000 is the model I own and it looks fine to me. As for games to recommend(I'll stick to mostly JRPGs since that's what you asked for):

Persona 3 Portable
Final Fantasy Tactics: War of the Lions
Ys I & II, Oath in Felghana, Seven
Valkyria Chronicles II
Gurmin: A Monstrous Adventure(more action/adventure and Zelda-like than RPG)
Sega Genesis Collection(features a lot of different games, namely Phantasy Star II-IV for your JRTG needs)
Mega Man Powered Up(great remake of the first game with 4 more levels and level editor)
Killzone Liberation(top down shooter, I find it more fun than the other games in the series)
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Ric1987: snip
Just thought I'd tack on Final Fantasy IV Complete Collection since I don't think it's been mentioned. It has the original game (well, enhanced like the other original Final Fantasy games released on the PSP so far), Interlude which takes place between IV and The After Years, and The After Years which follows some years after the original game. I always seem to find those games fun, except FF2 which can either be really fun or a really big pain.