I've had a lot of webhosts in the past. My current one is DreamHost -- I really couldn't be any happier with them. Very accountable, customer-centric, reliable, and straight-forward. Good deal. Lots of hosts have lame restrictions and rules and don't tell you when they go down, but DreamHost isn't like that. If you want a deal, btw, I can get you a discount code.
The big problem I've had with webhosts in the past is stuff going down. One thing I like about Dreamhost is they really sweat it and even have an off-site status page where you can check what's going on.
I would recommend buying a domain name separately, however. Any reasonable place is gonna offer dot coms for somewhere around $10. I'm pretty happy with godaddy.com for that, but some people say their support is bad. It's a good idea to get a domain name from a domain name company rather than your host, that way you're not limited in any way. Likewise, don't buy hosting from a domain company.
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Dan Grover
co-founder of WrongPlanet.net