-I've got all the new consoles and an older one: Sega Saturn, Sega Dreamcast, PS2, GameCube and Xbox. So know what I'm talking about when I say a console is good.
I really think the Xbox has a better design than the GameCube. For one the Game"Cube" isn't even really a cube, it's just a box...

-Yes the Xbox.com site does suck for the most part... There are a few cool things about it like the top banner/nav.

-As for the theme, I'd say don't over do the green, keep it black for the most part and use green as a highlight. The Xbox it's self is all black but the green thing on the top and the silver buttions and green power light. For the tool bar you might want to have it black with dark grey stripes.
http://xbox.ign.com/ has a better Xbox layout than xbox.com, you might be interested in it's design also.