PSP and PSvita games

so..im planning to buy a PSvita this xmas with my 13th month pay.....but idk what type of games will work on it (file formats), also got an old psp,.....anyone can give me an idea what type of files does PSvita support? (what is the format of psvita game)
also list of anime games for it (and for psp)
XD
any game is fine as long as its anime-related/made by Japanese developers.
give me as many as you can XD thanks

For Vita... well, you can start with Dragon's Crown, Persona 4 Golden and Disgaea 3: Absence of Detention. If you like beat'em-up, RPG and strategy games, they're all anime-based, and they're a lot of fun. Those are my personal recommendations.

PSP has such a wide variety of games, I don't even know where to start. Persona 3 Portable? Valkyrie Profile: Lenneth? Final Fantasy VII: Crisis Core? Tactics Ogre? God Eater? Monster Hunter? Seriously, the PSP library is hugimongous...

You can also get Atelier Meruru Plus and Atelier Totori Plus on PSN

thanks for the replies~!
really gave me some good ideas.....
does PSvita support ISO games(psp games)?

Don't forget Soul Sacrifice... And the upcoming JRPGs toukiden and Conception 2 also Danganronpa remix!
Edit to the OP: you can only buy PSP games in the PSN store. Doesn't have the small disk capability thing..

I use to have eCFW on my vita. I just update by accident and they keep removing the exploit games before i can dl it. Meh my psp is in the same case with me so i can deal until vita format cfw is out.

Wait until February for this:

-Monster Hunter(everyone plays this [size=10]but it's gooood[/h])
-Dangan Ronpa is getting an western release, take a look. It's an VN, puzzle, rythm/shooting investigation game. It's better than it sounds haha
-Final Fantasy Tactics, and Tactics Ogre(played FFT, playing TO. FFT is among my favorite games all time. It's strategy/rpg(duh), your thing?)
-BlazBlue(Anime-style fighting game. Is in my list, people love it...)

*Back to Tactics Ogre*