Warning.
Setting up a registered domain name or even a static IP for your personal computer/network is a very novel idea and one that I employ myself, but be wary. There are likely thousands of kids right now scanning every conceivable IP address available just waiting for that one novice to put up that one insecure box.
If you put up a web, ftp or email server, use a system that's tested and supported for serving as such. Don't, under any circumstances, use Windows 95/98/Me with Personal Web Server. In fact, don't place machines running those operating systems live on world network at all. i.e. Put as many machines as possible on non-routable networks (198.162.0.0, 10.0.0.0, etc).
If you're using Windows shares, unbind TCP/IP from the sharing service (use NetBEUI only).
Use a firewall, block access to every single port then open ports up individually as necessary.
Buy books on network security for whatever platform(s) you run and keep an eye on mailing lists such as BugTraq to keep up to date on new security hazards.
Good luck,
brendanc@icehouse.net