Just download every single demo they have on psn for starters :)

Sweet Man im getting the PSP GO!!!

instead of Hot Shots Golf get Pangya Fantasy Golf - way more fun.
DJ Max Fever or DJ Max Clazziquai Edition - best rhythm games on any platform PERIOD with great replay value,
Disgaea Portable - best srpg on psp so far with tons of replay value,
Burnout Legends/Ridge Racer 2,
Test Drive Unlimited/Midnight Club series(DO NOT buy NFS games, Juiced games - they're terrible on psp),
Tekken Dark Resurection or wait for Soul Calibur - i would recommend second option,
Phantasy Star Portable - way more accessible gameplay compared to Monster Hunter series on psp,
Syphon Filter games,
Socom games,
if you're into action jrpgs Tales of the World Radiant Mythology and Crisis Core are good,

Tales of Eternia, Final fantasy Tactics, Tekken DR, Metal gear solid portable ops+,FF Crisis Core,Megaman maverick hunter,God of war chains of olympos.

You'll def need an extra battery or an emergency charger otherwise you're going to be out of luck.

Get yourself God of War, WipEout and Resistance Retribution, all excellent games.

Maybe download a movie converter and stick a couple of movies on there (and some comedy) to keep you going. not to mention music of course.

Other slight problem will be reflection on the screen. if it's too bright where you are, you are going to struggle to see the screen. I use mine all the time when i go travelling, and whenever that happens i switch to listening to music.

Good set of headphones are a bonus too. PX100 are a good travel set.