Only the premium version is compatible with old xbox games, becuase all the emulators come stored on the hard-drive (the core version doesn't come with a hard-drive). Only xbox games that Microsoft have created emulators for are compatible (which is quite alot but not all, more emulators should be released when they're ready).
The 360 does not make xbox games' graphics' "better", but it does output the games in High Definition.
As for me, I'm a Nintendo Fanboy, always have been. It's the Wii for me, and I'll probably get the 360 aswell. Can't wait the Gears of War.