GoDaddy.com does seem to have an OK reputation. The key to their service is not to host mission-critical websites. If a site you want to build is a simple one that's not going to process a lot of traffic, I think its a good idea to try them.
As was mentioned before, make sure to register your domain name with a well known domain registrar. DO NOT fall for a "Free Domain" with 1 year of hosting kind of deals with web hosting companies as the domain is key to your business, so you want to keep control over it.
As far as hosting itself, there will be hundreds, if not thousands of companies that will fit your technical requirements. Question is - how do you pick one?
My personal suggestion is to do little research:
- do not go for the most resources for less price
- contact the company with questions you might have
- look into company history (how old their domain is, what is their reputation is like)
This will be a good guide to start:
http://www.hostingdiscussion.com/web-hosting-requests/1835-choose-your-host-carefully-users.html
Let us know if you narrow something down or if you have further questions.