I am evaluating Kubernetes (with Docker containers, not Kubernetes) and Docker Swarm and could use your input.
If I'm looking at 3 (8.76 hours) or 4 (52 min) 9's reliability in a server farm that is < 100 servers, would Kubernetes be overkill due to its complexity? Would Docker Swarm suffice?
Docker swarm will be able to meet your requirements. I recommend you start with Docker swarm as it is robust and very straightforward to use for anyone who has used Docker before.
For a Docker user, there are many new concepts that you need to learn to be able to use Kubernetes. Moreover, setting up Kubernetes on premise without using a preconfigured cloud platform is not straightforward
On the other hand, Kubernetes is more flexible and extensible. Kubernetes is older than Docker swarm and the community for kubernetes community is really big.