Just create a unit file that starts/stops/restarts/etc. the container.

what do you mean exactly? What is the tool that you invoke? Or you use systemd's container executing ability?

Whenever I've done this, I've used the system service's ExecStart|Stop directives to run a Bash script which handles starting/stopping the container (e.g. `docker run ...`) and any other setup teardown behavior that's appropriate.