I have my domains registered through GoDaddy but I don't use their hosting. If you need webhosting, send me a PM and I can give you the information. You don't have to have your hosting and your domain through the same place.
If you do use GoDaddy, do a Google search for coupon codes. I've paid about $6 for all of mine using codes.
You can also try www.name.com
which, I think, is owned by Google.
Anyway...you were asking about design, not hosting. Definitely search the forums. A lot of us do offer web design services, blog installation and customization, etc.