Do NOT use Kubernetes unless you really, really need a lot of flexibility in rapidly scaling up, and occasionally scaling down your services.
If you do need that capability, Kubernetes is invaluable.
If you don't, plain old Docker and Ansible is a much better combination. Kubernetes adds a lot of complexity that doesn't pay for itself if you don't really need that much flexibility.
Do you really mean plain old Docker or do you mean Docker Swarm as well?
I think Docker Swarm is necessary in the absence of Kubernetes to ensure that the correct number of replicas are running on your cluster. It would help with automatically spinning up new replicas when a few nodes go down, changing the number of replicas on the fly, etc.
"It would help with automatically spinning up new replicas when a few nodes go down, changing the number of replicas on the fly, etc."
I'm saying for small deployments even this isn't really needed. If one container dies, have monitoring to alert you and then spin up a new one manually when you get around to it. Obviously, your system needs to have enough redundancy with each kind of container that you can still handle the load after losing one.
It's only if you are changing the number of containers a lot that something like Kubernetes is needed. And I think at that point go straight to Kubernetes, I don't know if there is a scenario where adopting Swarm but not full blown Kubernetes is the right answer, because then you likely have to migrate twice. Once to Swarm, and then to Kubernetes.
If you do need that capability, Kubernetes is invaluable.
If you don't, plain old Docker and Ansible is a much better combination. Kubernetes adds a lot of complexity that doesn't pay for itself if you don't really need that much flexibility.