GoDaddy is suppose to have good service, but I found them to be more expensive that most of the other hosts (for the hosting service). If you go with them though, check revision3.com and look for discount codes. GoDaddy is a sponsor of theirs, and offers many discounts to viewers.
I just bought a domain and hosting through GoDaddy about a month ago. Its my first experience with doing my own website, but so far it seems pretty reliable. Excellent customer service as well.