I have 2 static ip's from my provider. I pay a little extra for them. I've never asked and they've never complained about me running server's from my 2 ip's. One ip is my home network which has some redirection going on to port forward to my linux box any port 80 requests. The other ip, I've used for a webserver for my RC club hcrcc.org. I also have another host setup on there using apache's virtual hosting for a RC helicopter event our club holds every year. That's at shag.heliaddiction.com.
AS far as getting that DNS entry, you only need to setup a hostname on godaddy, and the setup the A address to point to your static ip address. It's very simple todo as long as you have static ip's.