(I'm thinking low Power, low price, low noise)
Sounds like a job for a Mini-ITX to me...

Has anyone run into a problem running a dell laptop 24/7? (its going to be a dell cos I can get one from a mate for cheap as it doens't have a battery)
Oh well, if you have your mind (wallet) made up for this laptop... FWIW, I have been running a Toshiba with a dead LCD as a 24x7 server (squid, ejabberd, firewall, ssh and port forwarder to the internal email server) at my institute for close to a year now, no probs. And it's a 5 year old P4 2.8 with internal 40 GB HDD, so not one of the cool-running ones either. Oh, and it's my remote bittorrent client too (rtorrent, over ssh and GNU screen). Needless to say, it's running a stripped-down VL 5.8 Standard...

Now to serve files would I use ftp or ssl or ---? I like the idea of being able to transfer data to the server from my mate's computers. Ideally, I could get my girlfriend or parents to transfer files to me simply and I could just give them links to download my files.
For an internal LAN entertainment server you should set up a samba or nfs share, or perhaps even a streaming server. As an internet server, nightflier and M0E-lnx pretty much covered it.