If your looking at getting a domain name most of the web server providers will also sell you a domain name as well. It would probably be easier to purchase the domain name and the web service from the same place and occasionally they may even give you a discount if you purchase both with them (although there is nothing wrong with buying them seprate). Yahoo provides web space as well as domain registration and there are thousands of other websites that do the same. Just be careful of what you can actually do on the site and the bandwith they give you (none of the free sites allow you to run a business off their resources, at least none that I know of). If your looking at how to develop the site or need some other information about website development I found the following site to be helpful for many people:

www.htmlgoodies.com

Good luck with the site.