My servers were run on an old computer I had lying around my house. They were not any subset of prissi's or Timothy's servers. I had no setup that could allow anyone remote access to operate my server beyond nettool.
I cannot run my physical server at the moment, however, I am happy to help out with simple server chores remotely if someone else has hosting capability.
To host yourself, you need a computer that you will keep always on with decent ram (1 GB at least, I think), and a decent internet connection (always on, preferably a fairly stable IP, does not drop connection, 5 Mb/s up and down. Don't try DSL, you'll need cable or fiber). You'll need administrative access to the main router for port forwarding. Think also about any usage caps or bandwith charges, as every time someone joins a 1-4 MB savegame will be transferred. Processor doesn't matter too much, I ran my 2 servers on a 10 year old Pentium 4. These are the major hurdles, beyond that, PM me for additional little tips for hosting.