Check out
http://www.xbox-linux.org and
http://gentoox.shallax.com There is a forum here on X-S that talks about Linux (it's named *nix). And I would advice against the USB modem for broadband, Xbox is only USB 1.1 and I had so many troubles with a USB modem even on a USB 2.0 computer.
You should get a Ethernet Router that has a built in ADSL modem and at least 4 ports, you can get these very cheap now (everyone is getting wireless).
XBMC is great for showing videos, music and the like but Shallax also does a Linux port of Gentoo with MCE software if you want to use that (look into it at his site).
You can put a 300GB hard drive in but you will need an LBA48 bios if you are to play games. I'm not sure how to use the lot in pure Linux you will have to search on that (gentoox forums has loads of info

).
You can put a DVD Burner in but you wont be able to play original games, and I think it is slow to (Xbox bus is ATA33). Again shallax forum has a guide on this some where I think.
Since you are posting in the Smartxx forum I am going to say get a Smartxx

. It can even boot linux right of the bat. www.smartxx.com for more info.
The X2VGA is good but I think resolutions are limited in Linux I don't have one so I'm not sure. USB adapters are cheap to come by and are aprently easy to make. Plenty of tutorials on this.