Coolio.
My recommended game starter pack for you:
JRPG: Lost Odyssey, Tales of Vesperia (if you are in NA), Infinite Undiscovery, Blue Dragon and then wait for The Last Remnant
Platformers: Kameo, Castle Crashers, Braid, Castlevania SOTN and then wait for Banjo-Kazooie Nuts & Bolts
Adventure: Ninja Gaiden II, Crackdown, Dead Rising, Oblivion, Mass Effect and then wait for Fable 2 or Fallout 3 or Saints Row 2
I am assuming when you say adventure you mean action oriented or RPG is fine. You should give the normal staples Gears, Halo 3, BioShock a shot even if you dont like shooters as they are great adventures. Gears is not FPS but on a third person view.