To be perfectly honest, it is NOT worth the hassle. I used to have my own server running and you always had to have that computer running, plus with most providers your IP address is NOT static meaning it changes all the time. So you would need a program running on your computer that updates you domain name with the information. You can get free domain names that belong to the service you are using to point to your computer, like www.dyndns.org
. If you go there they can explain the part about redirecting to your computer.
As for the server part, you will need an OS that has the capabilities of being a server. WIN98 can do that but can only support 3 connections at a time( approx) and WIN xp can also do this.
The other thing to remember is that usually you only get so much bandwidth per month that you are allowed to upload and download, most companies do this to prevent people from running websites on a home connection. Also they sometimes block the ports that allow you to run a website.
If you go here you can get hosting for pretty cheap a year www.totalchoicehosting.com
You can even buy your own domain name with them it you want.
Hope that helps.