If it's only about solidity DigitalOcean, AWS, and similar are ok for running single-host instances of your dockerized apps. If you want to get into clusters and scaling or are looking for a way to just take care of your containers and not of the infrastructure anymore, there's not many ready-made solutions, though. Amazon is working on ECS, and Google on GKE, but both are in a very early invite only Alpha stage. Other than those two, there's currently only us at Giant Swarm (
http://giantswarm.io/) afaik. If you're interested you can register for an invite and if you contact me directly, I could get you the actual invitation a bit faster.
Also note that there's quite a lot of self-service solutions based on Mesos or Kubernetes, but then you're back at managing your infrastructure yourself again and you still have to book DigitalOcean or Amazon Servers.