This is a question that most people ask themselves when they first start.
There are so many options on google ( mostly misleading companies) that offer the service.
But its important to consider exactly what it is your after, where you live and what you're store specialises in.
Depending on what you’re after, I can give you two different solutions/ answers. But before I can answer that, you mentioned managed hosting. Would you like the hosting service providers to run the website for you and make all the updates on your ecommerce store for you?
Or do you mean, simply fix any problems that your service might experience?