If all of this seems too much trouble and you don't mind paying a hefty premium every month for it, all the big cloud players have some sort of container-based service offering. Since these vary wildly both in functionality and feature set, anything that would get put onto this page in that regard will probably be outdated by the time it gets published, and we are more interested in deploying services on our own, so I will leave you links to the appropriate offerings that will have up-to-date information if you choose this route:
- Amazon ECS: https://aws.amazon.com/ecs/
- Google Container Engine: https://cloud.google.com/container-engine/
- Microsoft Azure (Azure Container Service): https://azure.microsoft.com/en-us/services/container-service/
- Oracle Container Cloud Service: https://cloud.oracle.com/container
- Docker Cloud: https://cloud.docker.com/
- Probably many others that I have missed
Personally, I would recommend this approach for small-to-medium deployments due to ease of use and tested environments. If your needs expand past these scales, implementing your service on scalable groups of virtual machines on Virtual Private Clouds (VPCs) with the same cloud service provider is generally one of the ways to go as you can tailor your infrastructure in the exact way that your needs expand, though the upfront DevOps costs are not small, so decide accordingly. A good rule of thumb to remember with pretty much any cloud offering is that with easy tooling already provided you get much quicker deployments counterbalanced by increased costs (usually hidden) and lack of flexibility/customizability.