Domain name registrations are priced on a subscription-like model that allows a person or business to register that domain name for a certain period of time (usually in annual increments). At the end of the registration period, you (the domain name registrant) have the option to renew the domain name registration for an additional period of time, or let it expire. It is important to renew your domain name registration, or you may find that all of your work building traffic and views to your site ends up benefiting someone else (in the instance that someone else registers your domain name after you let your registration expire), and potentially costing you more in rebranding.
The first step to starting your website is registering your domain name. Think of your domain name as a street address for your website. Without a domain name, you would have to tell customers to visit your website at a temporary url such as 220.127.116.11/~yourwebsite instead of yourwebsite.com. Get your own domain name to lend your site a professional look and establish your online brand!
The practice of using a simple memorable abstraction of a host's numerical address on a computer network dates back to the ARPANET era, before the advent of today's commercial Internet. In the early network, each computer on the network retrieved the hosts file (host.txt) from a computer at SRI (now SRI International), which mapped computer host names to numerical addresses. The rapid growth of the network made it impossible to maintain a centrally organized hostname registry and in 1983 the Domain Name System was introduced on the ARPANET and published by the Internet Engineering Task Force as RFC 882 and RFC 883.
Make sure your Internet service contract allows hosting. Many Internet service providers (ISPs) expressly forbid personal hosting unless you have a business plan, which often costs significantly more than a standard use plan. This shouldn't be an issue if your site only generates a few hits per month, but any kind of significant traffic will draw attention to your hosting.
Beyond that, Dreamhost is a 5-of-5 hosting company for many reasons. They operate their own control panel, which is convenient and easy to understand. While phone support isn't available 24-7, they are responsive to chat and tickets. The company uses superfast SSDs for all their storage, has a free SSL certificate (for more secured web browsing), and provides SSH access for those plans that are intended for more technical users.