A fully qualified domain name (FQDN) is a domain name that is completely specified with all labels in the hierarchy of the DNS, having no parts omitted. Labels in the Domain Name System are case-insensitive, and may therefore be written in any desired capitalization method, but most commonly domain names are written in lowercase in technical contexts.
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."
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.
Under no circumstances should you pay more to transfer a name than to get a new one. Check what the transfer will require. Does the new service handle the task completely? Or do you have to go into your current registrar's site and change the technical details manually? Finally, check the transfer policy of the registrar before registering your domain name.
iPage's web hosting packages start as low as $1.99 per month and they throw in domain registration for free during the first year, which makes them a bargain for very, very lean startups or one-person operations. They also have the classic domain name search portal, and provide a tutorial on the new TLDs that helps, considering a new one seems to be appearing every second or two.
In order to register any domain, you must provide certain personal information that you may not wish to be publically searchable in the Whois database. Signing up for WhoisGuard is a great way to keep your registration data private. WhoisGuard acts as a "shield" for your searchable information, displaying the address, phone number, and email of the domain registrar (Namecheap, e.g.) instead of your own. Keep in mind that WhoisGuard is an optional security add-on that must be renewed separately when you renew your domain.