If your choice of CMS platform was foundational, and your selection of hosting provider important, the priority that you give your domain registrar is several orders of magnitude less important. There are many ways to register a domain, but typically you’ll either go through your hosting provider, or one of the big name registrar’s out there like GoDaddy.
By volume, GoDaddy is the largest domain registrar in the world. They surpassed Network Solutions nearly a decade ago, and though they’re privately owned and not obligated to do much in the way of reporting, the Wall Street Journal reported in 2011 that they sold a 65% stake in the business to a trio of big private-equity companies – KKR, Silver Lake Partners, and Technology Crossover Ventures for a reported $2+ billion dollars. If their name still doesn’t ring a bell for you, you might recall GoDaddy from their marketing –they usually have a SuperBowl advertisement of some kind.
Being the biggest name in domain registration and web-hosting doesn’t come without detractors. GoDaddy has been criticized over the years, often by competitors and former employees, as being in violation of various ICANN rules, particularly as they relate to domain name portability(e.g. the domain’s are difficult to port out). Another area that they’ve received criticism for is their “upsell” approach. If you’ve ever registered a domain name, or picked-up a SSL certificate through them, you’ll know exactly what I’m talking about. What starts as a simple domain registration, can easily (or even accidentally) become email services, web-hosting, private registration, managed hosting, premium listings, and more. They’re also known for their coupons – nearly everything that can be purchased through them has a coupon. None of this is necessarily a problem, but it is something folks complain (loudly) about.
As you might imagine, GoDaddy isn’t universally loved by the WordPress community. Having a wide range of clients, we’ve worked with many different domain name registrars. I don’t personally have a problem recommending GoDaddy for domain registration, and SSL certificates, but at the same time I’m not really passionate about registrars. I can’t recommend them for their web-hosting, let alone managed WordPress hosting, as there are just so many out there that do it better. Name registration, on the other hand tends to be a low-value problem to solve. At around $15 per year, there are probably higher-value things for you to focus your attention on. From my standpoint, I mainly care about what the Nameservers field says… this points to wherever your DNS hosting lives, and may point to GoDaddy’s name servers. Wherever those point, that’s where you can manage your DNS settings from. By default, that will be GoDaddy (e.g. ns1.godaddy.com, ns2.godaddy.com).
Some popular alternative domain name registrars that I’d recommend considering include, NameCheap, Moniker.com, Hover.com, Gandi.net (which includes free private registration), dotster.com, in addition to most web-hosts.