Saundra, godaddy is one of the cheapest out there for domain names. I use them for many of my clients. They do have a phone number, but it's not toll free. You can order your domain and just say NO to all of their offers.
And just because you got your domain name there, doesn't mean you have to host your site there - although they are cheap and reliable with that as well.
No matter who you use, print out all receipts and email documentation, and add your username and password. Even though you think you'll remember it, you may not down the road right when you need it most.
As always, feel free to contact me for free suggestions and assistance: email@example.com