My personal preference is to register the name directly with a domain name registrar rather than through my web host. I've heard stories, in the past, of less-than-reputable web hosts that registered the domain under their own name, making them the owner of the domain rather than you (although I don't know if such web hosts still exist today). Registering direct with a domain name registrar allows me to make sure that I am registered as the owner, the administrative and technical contacts. Being the owner is vital — if someone else places himself as the owner (such as your web host), he can always decide to charge you some exorbitant fee for the use of the name later, and there is little you can do. The various other contacts are less vital, but may still play important roles, depending on your registrar. For example, for some registrars, the administrative contact's approval is required before a domain name is transferred out of a web host (or at least, it used to be). If he/she cannot be contacted, the technical contact is used.
Domain names put a friendly face on hard-to-remember numeric internet addresses. Every computer on the internet has a unique internet protocol (IP) number. A domain name represents one IP number or more. For example, the IP number for the domain name whitehouse.gov is 220.127.116.11. The whole purpose is to give users an easy-to-remember handle so that when sending an e-mail to, let's say, the President of the United States, you can type firstname.lastname@example.org instead of the more unwieldy email@example.com.
Before you sign up for Web hosting and start building a website, you need to buy the domain name where visitors will find your site. Hundreds of different registrars sell domains, so first and foremost, know that domain names work the same no matter which registrar you use. You don't need to buy your domain from the same company that will host your site. Aside from picking a registrar -- and, of course, your site's name -- you also need to pick a top-level domain like .com or .org.
Premium domains (also known as aftermarket or pre-registered domains) are short domains, often just one word or even just 3-5 letters. Most of them have a .com extension but many premium domains end with .org, .net, and .biz. These domains include common words and are generally the most memorable. Because companies value short domains that match their company name or products, these domains are typically the most desirable. Additionally, certain domains sold by different registries are considered premium and therefore have a higher price point. In some cases, the renewal costs of these higher-priced domains are also quite expensive. Some high-priced premium domains, though, renew at a regular (lower cost) rate, giving you a better value in the long term. Make sure to research the overall cost of the domain plus renewal to find the right domain for your budget. You can browse Namecheap's premium domains in our Marketplace.