If you want to make your server public the easiest way I have found to do it is through
https://www.no-ip.com/
Just make a free account and download the little program for it (dont remember if you download it before or after you create your host) then click on add new host on the website and it should take you to this page
Put in what ever name you want for the hostname and select what ever you want for the domain. The only other thing you need to do here is put in your computers IP which can be found by going into the command console and typing ipconfig.
Once that is all set up you need to locate the hosts file on your computer, on vista it can be found here C:\Windows\System32\drivers\etc. Open that with notepad and put in your computers IP and the hostname including the domain you choosed.
It should look like this:
127.0.0.1 localhost
::1 localhost
69.225.107.98 randomservername.servegame.com
If you have a firewall or any kind of anti-virus or spyware program it may block you from saving it so you will either have to get admin rights or turn off those programs.
Almost done, in navicat you need to open the realmlist table located in the realmd database and set the address to your computers IP.
Finally open up the realmlist file in your wow folder and change it so it says "set realmlist randomservername.servegame.com" obviously put in your hostname and not the one I have here.