Most website developers or designers will register your domain for you, so you don't need to worry about the technical aspects of domain registration. But there are plenty of good reasons to register your own domain name:
There are two drawbacks to registering your own domain. First, you need to become a little bit familiar with how the registration process works, and how to set up your DNS entries (unless your web developer will do that for you).
Second, you may get junk mail through the post office and email from companies that will try to trick you into changing registrars or hosts. If you fall for one of these tricks, it can be a big hassle to straighten out. So the best course of action is to register your name with a cost-effective registrar, pay the renewal fee as it comes due each year, and leave it at that.
There are a lot of places you can register domain names for your horse business. These companies offer essentially identical service but the prices vary from $4 to $35 for a one year registration depending on the domain extension (.com, .net, and .org cost more). Since there is no difference in value between the services, I recommend choosing the company with the best prices. I register all of the domain names for my own businesses and for my clients at GoDaddy.
GoDaddy was one of the first companies to offer domain names at low prices, and they continue by offering specials for registering certain domain extensions. The fee for registering a "top level" domain name—such as the best choice, .com—is only $8.95, plus a $0.25 fee to ICANN (the global domain registration authority. That brings the total for each domain to only $9.20 per year, with added discounts for registering the name for longer than one year.
GoDaddy also has specials on the less-favored extensions, such as .biz, .info, and so forth. For example, those extensions have been on sale as low as $3.99 plus the $.25 ICANN fee. The low price makes it appealing to register your domain name with various extensions in order to keep other people from snapping them up.
(The link will open a new browser, so you won't lose your place on the Equinnovation website)