Two weekends ago, I took the first step in setting up my new roller derby website: I registered a domain name for it. Two, actually.
Choosing the right TLD (top level domain)
The site is for the roller derby practice group that I skate with. Since we're an independent, volunteer-run organization that's not trying to make a profit, I decided to register a .org TLD as our primary domain: pfmrollerderby.org. I also registered pfmrollerderby.com because I'm sure someone will forget whether we're .com or .org (since .com is such a "default" web-related buzzword for many people). I wanted to make sure we'd get the traffic from both domains, and I wanted to have more control over our "brand" by ensuring that no one else registered the .com version of our site.
Depending on how much money you want to spend and how much control you want to have over your brand name or domain name, you may want to register the same domain name with various other TLDs such as .net, .biz, country code TLDs (.de, .co.uk), etc. I'm cheap, though, and our group is fairly small and local, so I figured a .com and a .org were good enough. If you do register multiple domains, be sure to check back for my post on canonicalizing your domain name... once I get around to writing it.
Choosing the right domain name
A good domain name should be relevant, easy to remember, and easy to tell to someone else. Your domain name will often be the first part of your website that people see (e.g. on your business card or in search results), so try to pick something memorable but also descriptive of what people will actually find on your site. For example, if I do a search for [window blinds] and I get back search results from www.windowblinds.example and www.spirit.example, I may be more likely to click on www.windowblinds.example because their domain name implies that their site is very relevant to what I'm looking for. www.spirit.example might belong to the Spirit Window Blinds Company, but I couldn't tell that from looking at their domain name.
Of course, there are many counter-examples to this, in particular if you have a strong brand name. The domain www.google.com isn't very descriptive (www.google-search-engine.example would be much more so), but Google's branding is so strong that they don't need a descriptive domain name. Same with Twitter, Merrill Lynch, Sears... you get the picture.
I picked pfmrollerderby.org because I wanted to include my group's name (PFM Practice Squad) so as to differentiate us from all the other roller derby sites out there; but I also wanted it to be obvious that the site is about roller derby, since pfmpracticesquad.example wouldn't be very descriptive, unless you were already familiar with our group.
Registering your domain name
I forgot to mention that, during the previous steps, you'll want to use a service like WhoIs lookup to check whether the oh-so-clever-and-memorable domain name you've chosen is already taken. (Heads up: I don't recommend using Network Solutions to do this! Here's why.) Even though their marketing tactics are bizarre and irrelevant (what do NASCAR and bikini car washes have to do with web hosting?), I use GoDaddy to register domain names since they're relatively cheap and well-known, which I take to mean "reliable." $10 for a .com, $9 for a .org. You can register a domain name at a ton of places, and you don't necessarily have to register with the same company that you host your site with.
When choosing a registrar, look for one that allows you the most control over your domain name. They should allow you to host your site with a different company if you so choose, or to transfer your domain name to a different registrar and still retain control over it.
Next: Choosing a web host