The longer your domain name is, the harder it is for people to remember it and the more chance you have of someone misspelling one of the words. Most good single word domain names are long gone, but you can still avoid long domain names by getting a little creative. If you have a single word you really like that is not available, try adding an adjective or verb in front of it and seeing if those variations are available. Think of your domain name as part of your brand, and make sure it matches how you want people to think of you.
The suffix identifies the name as belonging to a specific top-level domain (TLD). As of late 2016, when this article was written, there are numerous TLDs available for general purchase, including .com, .edu, .game, .green, .hiphop, .net, and .org. The most popular of these by far is .com, which is supposed to indicate commercial sites, but in reality has come to include almost everything.
If you already have a web host, obtain from them the names of their primary and secondary nameservers. Don't worry if you don't understand what these things mean. Just save the information somewhere. The information can usually be obtained from their FAQs or other documentation on their site, usually under a category like "domain name" or "DNS" or "domain name transfer" and the like. If you can't find it, email them. You'll need the information to point your domain name to your website after you buy your domain. Having said that, if you don't have a web host yet, don't worry. Just read on.
Domain names are often seen in analogy to real estate in that domain names are foundations on which a website can be built, and the highest quality domain names, like sought-after real estate, tend to carry significant value, usually due to their online brand-building potential, use in advertising, search engine optimization, and many other criteria.