I've recently set up a Dell GX260 small form factor computer for use with minimyth, and it went painlessly. My config is P4 1.8 GHz, 512 DDR, Nvidia FX 5200 Video (Low profile)
I got the low profile card buy buying one that had a low profile card, and removing the vga port from the top and bending the backplate over. Worked a treat.
Everything "just worked" on the first boot, sound, net, video. It is silent (well we can't hear the fans spinning) and lives on the drawers at the end of the bed. Our 34cm CRT tv fits perfectly on top of it. We don't bother turning off the minimyth frontend, since it doesn't bother us while it is on.
You can pick these up cheaply on ebay (mine cost AU$81 with no drives or ram), just make sure you get one that you can afford to upgrade the ram to 512MB on, some of them use PC800 RDRAM which costs an arm and a leg. (GX240)
http://search.ebay.com.au/search/search.dll?from=R40&satitle=dell+gx260
