Guide: Running Jellyfin in Synology's DSM 7 Using Docker Compose

[Goby]

Also with this setup what is the easiest/most efficient way to update Jellyfin moving forward?

If you're using the "latest" tag for the Docker image, all you have to do is stop and rebuild the project to recreate the container with the newest image.
I personally specify a specific image tag. So I just stop the project, then edit the tag to be the newest tag, and rebuild.

Just make sure to always make a backup of the config folder in case you don't like what a new version does.

Actually with the Container Manager of DSM, you can go directly to 'Image" section and hit "Update". Container manager will stop automatically the package and perform the update. As long as you followed this Guide (Chache and config repo created in the docker repo) there is nothing to do.