This short article at “Smashing Magazine” has some useful tips for picking a domain name.

I would advise using a domain name registrar. Most web hosting firms will register your chosen domain name as well as host your site, but if you keep the hosting of your site separate from the registrar of your domain name, it will simplify making changes in the future. With this arrangement all you have to do is “point” to the host you are using for your site. Then if you move your site to a different hosting provider it’s a simple matter to log into your GoDaddy account and “point” to your new host provider. It’s like moving across town, the phone company flips a switch somewhere and your incoming calls are seamlessly routed from your old residence to your new.

I have all my domain names registered at GoDaddy. They usually have the best prices as well as many additional options you may be interested in. It has been my experience that they have excellent customer service, you can even talk to a real live human being if need be.

Tip: While there could theoretically be a "Joe's Diner" in every town in the world, there can only be one "joesdiner.com", so even if you don't think you want a website right now, it might be a good idea to register a domain name anyway, while you can still get one that you like.

Check to see if your ideas for your desired domain name are available.

DomainTyper is a dedicated domain name search tool, and GoDaddy has a domain name search tool on their home page.

This Wikipedia entry will give you more information on domain name registrars and this entry is a list of top ranking registrars. As you will see GoDaddy is far in the lead.

Also, if you decide to register your domain name with GoDaddy I can be of more help to you since I use them myself.