Don't use the same company as your registrar and host. It gives one company too much power over your valuable assets.
I use moniker.com for domain registration. They are in the same ballpark as most other low-cost registrars, they have a UI that is well-suited to those with mutliple domains, and they are completely professional. While they've gone through a series of acquisitions, I haven't seen their professionalism impacted.
For hosting, there are so many choices there is no point in trying to suggest one. For one, needs vary widely. I use a VPS at Linode myself.
I also use third-party DNS. I prefer not to rely on either the registrar or host for DNS. I use dnsmadeeasy. Again, these are valuable assets, and it is wise not to concentrate control with one vendor. As well, most registrars and hosts don't provide very good DNS service. dnsmadeasy (and similar companies) provide DNS servers located world-wide with AnyCast routing to the nearest server.
In each case, with these companies you are getting near-Enterprise level technology and support on a budget. Far superior to GoDaddy. Seek out similar companies.
If you are trying to save a dollar or two, you will experience a huge degradation in reliability and service vs. what little you save. Can you get GoDaddy on the phone? I can get each one of these companies on the phone when I need them. And I have - every one of them, and been completly satisfied.
You could also pay a WHOLE lot more to the top-tier companies (Network Solutions, etc.), and then THEY will call YOU! (Whether you want them to or not, LOL.)