As long as you have a robust enough box and a decent broadband connection, you dont have to buy or lease a server. In fact, over the long haul you are probably better off running one from home.
I had a really nice DSL connection when I started mine, when I moved and had to go with cable I made sure to get the "hispeed" hispeed connection. You pay considerably more, but the upload speeds are double. Your upload speeds are most important because you are broadcasting the server information to each player.
Minimum, I would have 2.4 or better processor (Intel P4's used to run much cooler than AMD, but Im not too sure about that now - I suspect AMD has worked on thier heat issues) and a gig of ram. I have removed myself somewhat from the tech world because of the family, so take my reco for what it is worth - a starting place.
I would look around at planethalflife dot com. Im sure I started there when I ran my server. Also, look around for some CZ forums, as they will probably have server administrators there who can help.
:::Also::: If you want to set this up behind a router I can probably help you, as with mine (Linksys) there is a bit of tweaking you need to do so the firewall doesnt block communication.