The first step in evaluation is to figure out what you need. Do you just need someone to manage the cloud or hosting environment, or do you need them to manage and support the application code and the hosting environment?
When you contact a managed services provider, get a feel for how intimately they will manage the application and what type of resources they have on staff. The more custom your application is, the higher the level of service you will need.
It’s hard for us to imagine taking a completely custom application and throwing it into a large-scale managed providers environment. Someone has to understand the application, how it is set up, and how it runs. Otherwise, when something goes wrong, you are likely to have an issue where the managed services provider simply blames the application and you don’t have a good way to get it back up and running.