Ive played Burst Limit once, rented with some mates when we were drunk as and I would pass seriously on that one, played a bit of Raging Blast at a mates house which was actually pretty fun surprisingly, just the camera is quite annoying at times.
Eternal Sonata is a good play, also could try Magna Carta 2, Tales of Vesperia, Lost Odyssey and that's about it for the JRPGs, don't bother with Star Ocean 4 or any Tri-Ace game out right now for that matter. I have a feeling you wouldn't like the western ones but give Dragon Age Origins, Mass Effect and Fallout/Oblivion a try.
As for general Xbox 360 games to get I would try Forza Motorsport 3, Modern Warfare 1-2, Assassin's Creed 2(Although you really should try beating the first so you know what's going on) Dead Rising, Halo ODST, Orange Box like everyone has said, Left 4 Dead series, and there's a ton of Arcade games you can get as well, Shadow Complex for example.