First of all, domains are so inexpensive now, as low as $8.95 for a year at GoDaddy.com. Web hosting is inexpensive as well. PowWeb.com has 2000 meg of space and free webstats for $7.77 a month. (It's really a good deal - some hosting companies charge charge twice that for only 50 meg of space and extra for website statistics.) So there is no reason for you not to have a proprietary domain name that is easy for the customers to remember. It’s the first thing in showing your professionalism and that your business is not just a hobby. Your web designer should be able to work with you to come up with the perfect domain name and do a search to find out if it is available and register the name.
Extensions: There are several categories of Internet domain names to choose from.
.com (commercial) most widely used extension
.net (network) commonly used by ISP's, Web-hosting companies or other businesses directly involved in the infrastructure of the Internet.
.org organization primarily used by non-profits groups or trade associations.
.biz used for small business Web sites.
.info credible resource Web sites.
.us American Web sites - the newest extension.
.cc originally the country code for Coco's Keeling Islands - now unrestricted and may be registered by anyone.
.bz originally designated as the country code for Belize, but is now used by small businesses who can't get the name they want using the .biz extension.
.tv rich content/multi-media Web sites, commonly used within the entertainment or media industry.
Technical: When you register your domain name, you pay on-line with a credit card and they will ask for your name, address, email and to create a password. If someone other than you does the registration for you, make sure the domain is in your name and has your email address as the owner.