I believe Dell and IBM both sell computers with XP or Linux on them. The programs you mentioned don't really take much power so you don't really need a high end PC. If you like iTunes (and use it to sync an iPod) then I would advise against Linux. There is not iTunes port for Linux.

I would think a Mac Mini would fit the bill. It's fairly cheap ($599 or $499, I didn't look) and doesn't really have any extra stuff. I'm not sure about backing up XBox 260 games, but iTunes, MSN, and Firefox are all available for Mac (although Safari is faster.)

They have Intel processors and BootCamp so if you end up needing Windows you can load it.