I would advise running your own rather than hosting, either on AWS or in-house. You will benefit from the knowledge and have far more control over the install (versioning, cost, sizing, plugins, etc). AWS allows us to have an image of our server made so that when we upgrade or test a new plugin, we can back out in seconds if there's a problem.
We paid iCampus21 to assist with our initial install. It was money well spent, and I believe we ended with the best of both worlds. A professional initial install that we now manage ourselves.