In that case I would say start with a Debian-based or Ubuntu-based distro of your choice. Ubuntu-based distros are also Debian-based, since Ubuntu is Debian-based. Mint is Ubuntu-based so it's a good choice imho. Mint should work pretty well for backups and Minecraft.

As a counter-example, Mint would (probably) be a poor choice if you want to turn that PC into a router or a DNS server, but sounds like that's not what you have in mind.

If you plan to Install more stuff in the near future, you could optionally look into containerization (Docker) which would allow you to someday swap Mint with another distro when you decide that you feel like changing. All of this, without having to reconfigure anything. Portainer might be a good soft-entry to Docker if you don't love the terminal, it gives you a nice UI. And it's compatible with Mint, ofc.

As for the fedi instance, it's a good exercise, you will learn a lot about networks. Personally I tried installing a Lemmy instance too, but I ended up turning it off as I realized that it didn't make sense for my use case. It just wasted bandwidth to stay in-sync with the rest of the fediverse.