Once you have chosen a domain name you will need to check to see if that domain name is available. If the domain name is taken by someone else then you will have to choose a different domain name. I use Godaddy to check the availability of a domain name and also to register domain names.
The above warning does not include companies such as Godaddy or any company which has domain name registration as their primary business and web hosting as a secondary part of their business.
Failure to follow the above advice could cause you to lose the domain name that you registered with the web host forever should you decide to change web hosts. This happened to me, and I don't want it to happen to you.
I recommend that after you register your domain name with Godaddy, sign up with a web hosting company and then point your domain name to the web hosting company name servers. That way you retain full control of your domain name. This is very easy to do at Godaddy once you know the web hosting name servers your site is assigned.