I can heartily recommend you something called Dokku, which more or less takes all the pain out of Docker. I had no experience with this, but got fed up of spiraling Heroku costs. Decided to slap Dokku on a €2.50 pcm VPS, runs like a charm. Multiple containers all communicating with one another, staging, production, failover environments, shared storage, all behind multiple SSL-secured domains.

Dokku is single-server only, however. So if you need a Docker swarm, you'll have to do that yourself :)