Amazon is offering free micro EC2 instances which, though a little slow, could be a heck of a chance to take a stab at Drupal for new folks while saving some cash. The EC2 instances are cloud-computing slices that offer burst speed for short-term high CPU demand, reasonable amounts of RAM, and even 10GB of storage through their storage service. Heck, you even get an "elastic" IP (essentially a static IP so you can point a domain at the server).
Turns out you can even setup a LAMP install. That sounds like a great opportunity! I wasn't the only one to think so, check out this great tutorial for getting going and running Drupal on a free EC2 instance.
Amazon's Cloud Website Hosting through EC2 servers is a great testing platform for Drupal if you want to try their free instance level. The cost to upgrade to a slightly higher instance level in order to handle mild production traffic levels is not terribly significant and the solution can scale with your organization as you grow.
If that all sounds like a bit too much effort, managing your own servers isn't usually a core business competency, Daymuse offers Managed Hosting.