If your ISP does not issue static IP's, the you can use a service like: /http://www.dyndns.com
is free if you use one of their domains while ods.org
charges 5.00 / yr for one of theirs.
For custom domains ods.org
is like 20.00 / yr for dns and 45.00 / yr for dns and domain registration.
it's like 27.50 and 42.50
As for the server name, when you register a domain name it will be something like domain.org
So your server hostname would be server.domain.org
The gateway and netmask should be the same as you are using now.
If you have a personal router, you will need to set your router to forward the correct ports. My router has a setting called "Virtual Servers"
where this is done.
You will need to know if your ISP is blocking the needed ports. If they have a policy against running servers, they probably will block them at the their router / modem.