Are you keeping it stock or doing CFW on it?
It's a 3000 series so I am not sure how easily that model can be hacked. I plan on getting a 2000 series down the road for modding purposes. I am assuming that is what you meant by "CFW"
You can install CFW on a PSP 3000 in around a second. It's literally a program you run to activate. Turning the system all the way off will reset it back to normal, running the program again will install the CFW.
KH: Birth By Sleep is a fantastic game. Gameplay-wise it's a sequel to Crisis Core but story-wise it's a prequel to all the Kingdom Hearts games. It's really just a rip-off of Star Wars.
Crush is a really good puzzle game. You know how Super Paper Mario had that 2D to 3D ability that was never really used well? This game uses it EXTREMELY well.
GTA Liberty City and Vice City Stories are NOT ports of the PS2 games but entirely original games set in the same cities and starring familiar characters. They're very well done. I prefer the original Chinatown Wars on the DS.
Half-Minute Hero is an amazing JRPG parody that moves at an amazing clip and is almost puzzle-like in some parts. It also has three other play types that aren't quite as fun as the main game, but are still good.
God of War: Chains of Olympus and Ghost of Sparta are surprisingly good entries in the GoW series. They don't do anything different. If you like GoW you will like these games, if not they won't change your mind.
Metal Gear: Peace Walker is great. Portable Ops kind of sucks but they came back with a vengeance and made an amazing Metal Gear game. Speaking of which...
Metal Gear Ac!d is a great MGS card battle game. It sounds crazy and it is crazy but it f*cking works. There's a sequel with a really weird art style that is still a pretty cool game to play.
The Sony original IPs are all fun:
LocoRoco 1 and 2 and
Patapon 1, 2, and 3.
Capcom dropped a lot of amazing games here, too.
Darkstalkers,
Ultimate Ghouls and Ghosts,
Mega Man: Powered Up and
Maverick Hunter X,
Monster Hunter Freedom,
Freedom 2, and
Freedom Unite.
There's a lot more. The PSP is a fantastic system.