First of all, congratulations on fixing your PC and on getting a lovely Xbox.
(Pssst - watch out for Dasilvsie, he might just pan you out of jealously because he's been pining for an old Xbox himself).
As for which games to get, on the top of my list for you are
Psychonauts and
Jade Empire. If your PC can handle it get Psychonauts for it (though it's just as marvelous if not more so on the Xbox, because you can simply sink into your sofa and play it that way).
Jade Empire is Xbox exclusive; if you loved
KOTOR you'll love it, you can get lost in the ancient mystical world of a China inspired RPG world in 3rd person 3D, and it has many little, often touching optional stories to find via side quests. I also recommend
Fable, another action/RPG with a different, more dynamic, kind of morality based system.
Not sure if you're into 'pick-up-&-play' racers, but you should definitely go for Project Gotham Racing 2. It's beautiful and there's plenty of things to do. I've also heard good things about Forza Motorsport, though I've only played the demo.
KOTOR II is great, but quite flawed and lacking in conistency in quality because it was rushed to deadline, but still very worth getting (though you can get the PC version, too).
Crimson Skies: High Road To Revenge is awesome if you're into Indiana Jones style adventuring but with retro-futuristic airplanes and lots of dogfights.
You'll notice right away the difference between experiencing games on a PC and on a console. PC games tend to be more 'formal' in that you sit upright in your chair, and the worlds seem more intricate and demanding psychologically. Console games, on the other hand, are very, very convenient for just picking up and playing. You can just grab the controller, collapse on the sofa with a cold drink, and jump right into the game.
