Finally got myself a PSP, now would like a good list of games to get.

[Reasonable]

I'd say a nice mix of genres would be served up with the following (ignore genres you don't like):

innovative IP and handheld funkiness : Patapon & Locoroco
console games in the palm of your hand : Daxter (platform fun), Ratchet & Clank (platform & shooting fun, God of War (violent mad God action fun), Wipeout (futuristic racing) , Silent Hill Origins (horror) and MGS: Portable Ops (action stealth strategy)
RPG : Jean D'Arc (I'll ignore FF as you said you didn't like it) and the many other titles already listed.

I also have GTA but again you said you didn't like that, and I'll leave out the more 'average' games I seem to have accidently ended up with.