There is a lot of talk out there about which is the "Best Web Hosting" company. With such a highly contentious subject (since being the "best" means more customers - and implicitly more money), there are a lot of "authoritative sources" out there. One authoritative (without quotes!) source would be Netcraft, but then again, their statistics are somewhat limited in this space - it is nice to know who were the fastest or who had the smallest downtime, but this doesn't tell me anything about pricing, customer support and other services (for example DDoS resistance/mitigation can be quite important these days!).
So, how to choose? I have just two words - very carefully. Have a clear goal in mind (ie. "I want a CMS" or "I want a blog") and try not to overestimate your needs (especially if it is a personal project). The most important thing is to own a domain (yeah, I known, look who's talking) - which you can redirect later on if you decide to move providers. I'm a great fan of niche/dedicate hosting (like Blogger, Wordpress, or why not - Squarespace). Given their specialization they can deliver their core competency very efficiently and securely and very often free of for a low cost. The second best thing would be a (managed) VPS and only in the last instance would I consider shared hosting.
Full disclosure: this is a paid review from ReviewMe. Under the terms of the understanding I was not obligated to skew my viewpoint in any way (ie. only post positive facts).