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."
If you're having trouble finding a domain name (whether because of crowding or cyber-squatters), check for a help facility on each registrar's site. Domain registrars typically house search engines that return a listing of available names similar to the one you want. When you search for a domain name at Namecheap, for example, you get both the status of that name and a list of suffixes available for that name. Maybe [Sitename].com isn't available, but [Sitename].biz or .org is.
A domain name is an identification string that defines a realm of administrative autonomy, authority or control within the Internet. Domain names are formed by the rules and procedures of the Domain Name System (DNS). Any name registered in the DNS is a domain name. Domain names are used in various networking contexts and for application-specific naming and addressing purposes. In general, a domain name represents an Internet Protocol (IP) resource, such as a personal computer used to access the Internet, a server computer hosting a web site, or the web site itself or any other service communicated via the Internet. In 2017, 330.6 million domain names had been registered.
Registrars offer a wide variety of registration durations—one year, three, five, and even ten. Be careful about registering for more than a year, though. First, there might be restrictions on your ability to transfer the domain name should the registrar give poor service. Second, the registrar could go out of business, leaving your domain name without a host. Check the policies closely.
The dispute was over the innocently-named Site Finder Service, launched by Verisign in 2003. With traffic to every .com domain going through Verisign, the Site Finder Service redirected anyone accessing an unregistered domain (via a typo, for example) to a Verisign website with sponsored links. The company argued that this was more useful to Internet users than seeing a generic error page. Whatever their reasoning, this made Verisign the de-facto owner of every unregistered domain (what else does it mean to own a domain?), and skyrocketed them from 2,500th into the top 10 most visited websites. The best part? Verisign launched this without running it past anyone.
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.