Getting A Domain Name
A domain name gives you a permanent address. If you get sick of your web host and want to move your site, you can do so seamlessly if you own a domain name. Your visitors will never even be aware that you've moved. Additionally, your email address will be permanent, no matter what local ISP you may be using at the moment. It means you can have both website and email address printed on business cards and on letterhead without worrying about changes.
Whatever you do, try to get a .com address. While the .net or .org addresses are perfectly valid, a certain percentage of people who type the address directly into their browser will automatically add .com to the end.
Domain names used to be strictly available from Network Solutions, and were always $70.00 for the first two years. Things have changed though, and prices have dropped considerably. You'll probably have to shop around as the prices are changing all the time. Here are a couple of domain registration companies:
000domains.com - Powered by OpenSRS from Tucows, so they should be around for a while. They have an easy interface, and are one of the lowest priced companies out there at $13.50 per year.
Or try the Domain Name Buyers Guide for rankings of many of these companies. They look at the terms of the contract, price, and give you consumer warnings if they see a specific problem.
Look for a site that's easy to navigate. No point in driving yourself crazy trying to figure out how to make changes.