To the thread starter :
Running a server at home, with a dynamic IP, is fine (as long as your connection is stable and you don't plan to host critical services)
Make sure to set correct DNS records for your domain. Since you have bought a domain name, your registrar must have an interface for you to do that, and it supports ddclient or equivalent (Or you can use freedns.afraid.org like someone already stated).
ddclient is fine for updating your DNS with your actual IP (works with dyndns, n*meche*p and many others)
Also very important : security
Only open the ports on your router to you server when your system is secure.
Suggested distros for a home server : Debian, Ubuntu server, CentOS, OpenSUSE...
Useful software : fail2ban
other : howtoforge.com has nice tutorials