Deploying Sitefinity external to the organisation

Hi there,
We are considering selecting Sitefinity as our preferred CMS. We have a project starting up for rebuilding our website and all web applications. We will be hosting our website externally at a third party, but all development and testing will be done in-house.

What we will have is:
- Our production environment, including Sitefinity will be hosted externally.
- Our Test and Dev environments will be hosted internally.

We want to have a Test environment with Sitefinity running, and be able to push content published from our Test environment to our Prod environment sitting externally to the organisation.
Similarly, there will be a Development environment.

Is this possible? If it is, is a set up that is recommended or supported? and please tell me if there is a better way of doing this?

Our business is a small one, and we do not have 24 hour support team to ensure the site is up and running all the time. This is why our solution is to host the site externally within Sitefinity.

Thank you for your feedback.
Rita