Okay, since there was no other suggestion, I've started by setting up a Samba/Windows share on the server, that can be accessed over the local network.
People could use it to pass around data in the hackerspace, or store things or such.... It's accessed at //LEMONADE/storage (or //lemonade.local/storage depending on your system and whether avahi has been installed). Using the ZeroTier network I mentioned before, can connect to it from anywhere in the world, works pretty fast as well!
Would love to hear if you have any comments.