One server choice is Windows Home server, that is for sharing files and having backups. I am about to start building one for myself. Servers can do a lot of things and it largely depends on the task. If you are interested in getting a gaming server, then you would need to get one with a better processor/memory, but if you were interested in a file server, then you wouldn't care what kind of processor you had, you'd just want a lot of hard drives.
For most uses, you would not need a very powerful server at all. I could probably get a file server running just fine with a Pentium 3 or greater processor. One thing you want to make sure, however, is that the server has a fast connection to the network. You do not want to have anything slower then 100mbps, but you'd probably want 1gbps. If you are trying to run an intranet, where the 4-5 computers would make requests to it through the browser, then you wouldn't need as fast of a connection.
Servers can be hard, or they can be easy. You never know if everything is just going to work or if you will need to spend hours troubleshooting. Running one of your existing computers as a server would be a lot easier then setting up a dedicated one. But dedicated servers are so much nicer :D