Host Gator is very expensive to sign up for a domain compared to others. Isn`t it better to go with a host that offers free domains or a less expensive one?
I registered with Yahoo. It cost about $13.oo per year including the "keep it private" feature. I definitely recommend the "keep it private" feature.
Free services generally entail an obligation to the hosting company. They may give away free domain names in exchange for you running advertising on your site.