Hosting a site at home usually isn't a good idea. A home internet connection is hardly suited for serving up web pages. If you end up getting even 50 concurrent users online at a time, then your site will probably buckle.
Some ISP's won't let you host a site, but sometimes as long as you stay within your bandwidth limits they don't mind. If you don't have a static IP address (usually you have to pay your ISP for them), then you'll have trouble routing your domain name to your computer (there are sites like
DynDNS that will update it automatically while you run a small program in the background.)
Running a server takes a bit of know-how too, search Google for setting up an IIS server, or Apache.
Your best bet will be to purcahse hosting from the pro's. Hosting is a big business these days and you can get it for literally a couple dollars a month.