SELinux in Podman works pretty much the same way it works on Docker, so if you are having problems with Podman, you should also be having problems with Docker, so I don't see how that's impeding your migration. You need to be more specific about the issues you're having to get a good answer.
The post by Chris Smart you linked on your comment below is a good start, but everything there also applies to Docker, so if you still didn't know those basics, you shouldn't be able to use Docker on Fedora either.
About your question of how to set it up, use-case is an important consideration, there is no generic answer that covers all use-cases. I've even found out that for some use-cases (like ad-hoc containers), disabling SELinux within the container (with --security-opt=label=disable) seems to be the most secure option. That's what I've done in contr (see this commit message). I've been meaning to blog about that, but never did because I'm in the process of migrating my blog but too lazy to finish it.
I've put a lot of links about SELinux in containers in this issue.