Only things to check for is depending on your provider they block common ports like dns, ssh, telnet, ftp, http services to your IP. Best way to test is start a server like apache if installed and try to connect to it from a remote location on the internet. If you cannot then make sure you have your firewall open for port 80. Also if a router is in between modem and computer make sure the port 80 on the external IP is forwarded to the lan machine that is running the service port 80.
If you have it all open and you can do a http://127.0.0.1
and the default apache page pops up. Then goto a remote site and see if you can get to it. Also you can use a port scanner site like this to see if port is visable. http://www.hackerwatch.org/probe/
If all is open and you can't get to it then you need to register a domain at say dydns can do it for you.
Also you need a static external IP. If it is dhcp assigned then you need to go with one of the free domain reroute services like dydns.
Worst case it will cost you a little more from your provider for an assigned IP and allow to run daemon services.