I'm a big fan of the PSP, and my favorite games are Silent Hill Origins, Burnout Legends, SOCOM: US Navy Seals Tactical Strike, and Metal Gear Solid Portable Ops.

If I was you and could only buy one game, I'd totally go with SOCOM.  Not only do you get to do cool wartime single player missions, the online mode is a full-force open arena like Halo or any other cool shooter game!

 Second to that would be Metal Gear Solid.  I'm a huge fan of this shooter/stealth series, but the SOCOM online mode makes that game the best bang for the buck.