Honestly, it probably doesn't matter. Most websites don't generate enough traffic and most site owners significantly (no wait, there's not enough emphasis there) SIGNIFICANTLY overestimate how popular their website will be.
Focus on content, get it up somewhere (anywhere) and migrate when the time comes.
All of the suggestions above are random generic shared hosting services and should perform similarly, except ServInt, NearlyFreeSpeech, Mediatemple, and RackSpace Cloud.
Short descriptions:
ServInt: Is known as the "budget RackSpace." They have an excellent reputation and great support, but you will pay more than an unmanaged server from another (quality) company for a worse performing machine. They are a top-tier provider and you cannot go wrong with them, but they aren't the best. A VPS solution from this company will perform better than a shared host, but you will be soft-capped on performance and will require intervention to scale. I have personally used this company in the past.
NearlyFreeSpeech: Is a pay as you go service. They pretty much pioneered this model and is a good value for low traffic, static content websites. For a low traffic website you could pay just pennies. Unfortunately, their rates are not competitive as traffic goes up and they did recently raise their prices. They utilize a custom cluster setup with redundancy. Your website is actually distributed so there is not an obvious single point of failure as typical with a shared host. I have also personally used this company in the past. I noticed their cluster implementation was a little buggy (within tolerance I suppose), where it would take a little while for website updates to propagate to the other servers, so it was possible for me to sometimes still be served an old version of a webpage. The upside is that your website is going to scale well and require little intervention besides keeping enough money in your account (it is prepaid).
Mediatemple: People tend to have a love/hate relationship with this company. It is not "hands down" the best in VPS business, but they have a quality product at a low (although somewhat dubious) price point. Their model is providing scalable (cloud-based) web hosting at a shared hosting price. They've had some trouble in the past with the reliability of their technology, but a lot of this was to do with the fact they were one of the first in the industry to offer these services. As far as I know most of these problems have been resolved. Service from these guys will scale much better than shared hosting, but at a much better value than NearlyFreeSpeech. They also provide a better upgrade path should your website get *really* popular or if you need to run custom software. I haven't heard anything recently about their support. I have not personally used Mediatemple.
RackSpace: They are the industry leaders in the web hosting business. They have a long standing reputation for having the best support in the industry. You will always be able to pick up a phone and get a real, qualified person on the phone 24/7 instantly. Their flagship product is in managed services, and historically they've also been the most expensive. Recently they have entered the mainstream market with their RackSpace Cloud offerings (and acquisition of Mosso). Their Cloud Sites product is most similar to Mediatemple's services, but it is bit more expensive (but still an excellent value). Cloud Servers and Cloud Files are more for people that have a little bit more know how, but provide a good platform for unlimited automatic scaling. I have personally used RackSpace.
All the others mentioned above: Will perform similarly with average performance. Support will vary by company but think of how much money you make, then think of how much you're paying them. If your website gets popular enough you will see performance degradation and hopefully their process for remediation is smooth.
(Other company I felt was worth mentioning):
MediaLayer: They have an excellent reputation for performance. While your typical shared host is a budget provider MediaLayer goes an extra step to keep speed as a very high priority. I have known people that have been very happy with these guys because their pages load lightning fast, this could be especially important in a world where attention spans seem to be getting shorter. They are a little bit more expensive, but not too bad especially if you like Google load speeds.