It's actually really simple to set up a Web server at home. I'm going to use this while I'm away at college to host game servers, have an offsite file backup, and share files with friends. Since the PC hosting the server will be at my house and I will be in my dorm room, obviously I can't just walk over and start changing system settings, so we'll need some kind of remote access.
Also, obviously, you'll need a dedicated PC, one you can leave running and leave connected at all times. What good is a server that goes down all the time? This PC doesn't have to be great, but remember, the more you run on it, the faster the PC needs to be to not lag (duh).