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I just did the same thing, I didn't want to buy the domain and the hosting from the same comany so I bought my domain at http://www.namecheap.com/ (8.88$/year), didn't have a problem and the domain propagation was much faster than I expected. Another place I found that has good reviews for domain registration is http://ev1servers.net (6.49$/year) but it has less features than namecheap.
Well, I have mine hosted by Yahoo for $9/month, and they throw in the domain name. A lot of hosting services do that, so you might be able to find something better if you shop around.