Hi,
Well in your case, the only ip you are paying for is your internet ip which you get with your internet connection. As you have mentioned, that is a dynamic ip and so can change at any time.
To have a way of always being able to address your computer/server you need to use the dyndns.org address which always points to your internet ip. dyndns.org is free to use if you want to use an existing address they provide like mine.nu. They charge like $20-30/year if you want to buy your own domain and have it point to your ip, ipickedmyownname.com (that is just the pointing of the address, not including the cost of the domain name) . You also need to run a daemon which updates your internet ip at dyndns.org. there are some free programs and some that cost money.
Make note that I use 'local ip' and 'internet ip'. So even though you have a dynamic internet ip address, you can have a static local ip. There are many ways to have your own local network, but most likely you have a linksys, netgear, belkin router. Make note of the ip address to your router, linksys is http://192.168.1.1 . When you type that ip into your browser, the router admin page comes up. make note of your specific router ip as that is your gateway used below.
Regardless of what OS you use, you will need the same basic info. The local ip address you want to assign to the computer, the gateway described above, the subnet mask and the dns servers from your isp.
There are far more better sources for windows networking, but here is a pic to help you put in that info.
windows networking
use the same subnet mask as i have, to find your isp's dns servers, goto the windows command line and type 'ipconfig /all' you can have 1-3 dns servers, so just write those down and put them in where needed.