Please be sure to research very carefully before going with any hosting company. I just had a client who was with a very well known cheap hosting company and when she canceled her hosting to move to someone else she found that that all the domains she had purchased thru this hosting company were not hers.
That's right, the hosting company bought the names themselves and she was only listed as the admin contact. When she canceled her service she lost ALL of her domains.
Some of those build your own sites also make it pretty tough to move your site (ok they make it impossible).
Another problem (especially for Wordpress or similar sites) is if the host has too many sites on each of their servers. I have seen cases where your WP dashboard access was spotty because all the available memory on the server was being used or the site would load very slowly at times due to this same issue.
I have recently moved my own site to
Bluehost after having my site hacked via a security flaw on the side of my hosting company. I have been recommending Bluehsot for a year or so and have never had any issues at all. Their support is second to none too. I have spoken to a real live person on the phone on a Sunday night! Price wise they are very reasonable too ($6.95/month) and you get one free domain name. They also have one of the most inclusive cPanels I have ever used. You can access everything about your site including your domain setup from one screen.