At its simplest:
docker run -d --name servicename --restart unless-stopped container
That’ll get you going. Youi’ll have containers running, they restart, etc. There are more sophisticated ways of doing things (create a systemd file that starts/stops the container, use kubernetes, etc.) but if you’re just starting this will likely work fine.
Yes - they’ll start automatically. There are other options for “restart” that define the behavior.
You can give whatever you like to “servicename” and use that rather than the ID.
For example:
docker run -d --name mysite --restart unless-stopped nginx docker stop mysite docker start mysite