Your personal contact information is registered to your domain and can be found in the public WHOIS directory. However you can keep your personal contact information private by utilizing Bluehost’s Domain Privacy. Domain Privacy will replace your personal contact information with Bluehost’s contact information. Using Domain Privacy helps protect you from spam and identity theft.
FatCow has one of the cheapest offers for an entire website package, with hosting and domain names for just thirty cents during your first month. After, that the price is $10.99 a month or $59.88 for the whole year, in a shared hosting package with enough bandwidth for most people. This is a limited promotion I found, but they still sell fairly well-priced packages (their "fat" options come with extras like marketing and advertising credits), and will gladly offer you perks for transferring your domains and hosting to them.
There are tons of great domain names available for registration and it can take as little as five minutes to register one at any domain name retailer. These online stores make it very easy for you to search for available domain names with name suggestion tools. They also offer complementary services, such as Web hosting and website design so you can register your desired domain name and set up a website all at once.
For the most part, you can pick whichever TLD you prefer, though a few have restrictions -- you can't buy a .edu domain unless you run an accredited post-secondary school. Many, but not all, country-specific domains (.us, .uk, .jp) are restricted to citizens of the country in question. Unrestricted country domains are often used for "domain hacks," where the extension becomes part of the title, such as YouTube's alternate address, "youtu.be."
There are organizations that are called registries that manage each TLD option. When you register domain names, you would first visit a domain registrar who would in turn check with the registry that manages that TLD to see if the domain is available. If the domain for the TLD you want discovers that it is in fact available, the registry adds it to their registry and gives you access to it. If the domain has already been registered by another user for that TLD, you will be shown during the domain registration process that the domain isn't available.
Dotster.com — This registrar provides fairly cheap domain prices ($15.75 plus 20 cents per domain), a convenient web interface to manage your domains, an optional privacy facility where your domain name is registered in the name of a proxy company, etc. They offer .com, .net, .org, .biz, .info, .us, .ca, .tv, .name, .cc, .de, .sr, .md, .co.uk, .us.com domains, etc. If you're transferring a domain here from other registrars, the price is even cheaper ($6.99 plus 20 cents). Both credit card and PayPal payments are accepted here.
Even if the term isn’t trademarked, don’t buy domains that are just a variation of another domain name. This means avoiding plurals if the singular is taken (mediatemple.net vs. mediatemples.net), hyphenating a phrase (media-temple.net), or adding “my” or some other preposition (mymediatemple.net). Alternately, you might consider buying these variations yourself and set them up so that if someone types one of the variations, they are redirected to your main site.