I don't think that Kubernetes is the most important thing on prod. Some colleagues from another team at $WORK use plain Docker and "orchestrate" their containers with simple systemd units that run `docker stop|start`. If the app is only a single container, that should do it. (Actually, in that case, I think that `rkt run` would be better since the process runs below the same cgroup, and systemd can detect crashes and restart the container.)
Anyway, Kubernetes is not so important for small deployments, but what I've found really helpful is CoreOS: an auto-updating base OS that gets out of the way and (more importantly) ships a combination of Linux kernel + Docker that usually works really well.