Domain registration is the process of purchasing the web name for your blog (such as www.blog-installation.com).  You may purchase domains in groups for a discount.  The longer the term, the lower the rate as well.  We use GoDaddy.com for all of our domain needs.  The interface between GoDaddy & HostGator works perfectly and we are very pleased with the combination.  Be advised that GoDaddy & HostGator usually link within an hour or two and we cannot vouch for how long other services take.  That being said you are more than welcome to use whatever registrar you prefer.