A great idea is to get on the playstation store and download any demos that look interesting. There are some great PSN exclusive titles that are available for purchase on the online store. Make sure to check the Special Offers section under New Releases every week after tuesday night, there's usually quite a few games on sale there. If you like online multiplayer, Fat Princess is a great exclusive. But that's all digital download stuff.
For your first disc-based game, it depends on how much you're willing to spend, and whether you want brand new games or older ones. Also whether you like single player, or online multi-player.
-->Single Player: Heavy Rain (dramatic), Infamous (cheap n cool), (any) Ratchet & Clank game (cheap n fun)
-->Multiplayer (online only): Mag (newer+256 players), Socom (realistic and better than people and reviews say+ REALLY cheap!!), Warhawk (classic PS3, really fun, also really cheap)
Resistance, Resistance 2 also have great single player modes and awesome multiplayer as well, and both are pretty cheap now.
Also Resistance 2 and Warhawk are two of the only PS3 shooters that have split-screen online multiplayer, if you plan on playing with friends.
Demon's Souls, Uncharted series, Little Big Planet, all great too. Too many great choices.

Gamestop Power Saver deals right now: Resistance 2 $13.49, Socom $6.49!, Unreal Tournament, $4.49, Demons Souls $29.99, 3D DGH $29.99.