Andy,
My XBOX is fairly quiet, I bought second hand and pre-modded with an Xecuter 2.2 Lite mod chip. It works pretty well, I have upgraded the hard disk to an 80GB drive, the dashboard replacement (like a menu program) I use is called Evox.
The actual program I use for playing my media is XBOX Media Center (version 1 I think) which can be found at .
http://www.xboxmediacenter.de/.
It is possible to get the XBOX Media Center to start up when you turn your XBOX on, it has different skins and can play all sorts of media including MP3 and WMA audio (not sure about OGG, I think it plays), Windows Media Video, Divx & XVID Video, MPEG 1 & 2 Video, Realplayer video.
Once useful feature I use on it is to play shoutcast audio streams over the internet, it will also play any music stored on the XBOX Soundtracks which can also be used in some games.
In general its pretty quiet, didn't cost too much (paid £150 for mine pre-chipped). You can buy XBOXes new pre-modified from some places online, I think one of the best is from a guy called Bald Bouncer (do a search on Google for it). One other thing I like about using my XBOX like this is the fact I can play DIVX streams with Dolby Digital audio and it sends it out in all its digital quality using the optical out on my scart cable straight to my DVD player which happens to have optical in

If you did go down the XBOX route, I would also suggest getting an XBOX remote control, they work well with XBox Media Center.
Other than that, have you considered a MiniITX motherboard, suitable case, hard drive etc? (although this is a little more expensive than the XBOX).
If you need any more advice, let me know.
Rob