How hard is it to move Docker containers to another system?

Or another container type if there's a better one?

My server was originally connected to my TV to run Kodi and play some games while serving files, so it's running Xubuntu. While it works well for the most part, I want to set it up properly, and be able to move the services to a new system when the time comes.

I was thinking that Docker, or another container system, would probably be best, because as well as hopefully being able to be moved, installing new software shouldn't affect anything else.

Am I on the right track? Can containers be moved to another system without needing to be set up again?

I'm running the *arr suite two Java Minecraft servers Plex media server Two copies of qBittorent NZBGet Ombi Mylar Codex and probably some others that I've forgotten.

While I'm at it, is there a best OS to base everything on? Preferably free. The server is a 4th generation i5 with 32GB RAM, and currently about 10TB of HDD space, with a small SSD for boot, and a Quadro graphics card for transcoding.

Thanks in advance :)