Im no expert but for your set up it sounds like you will need a central "server". Distributed syncing will not work as all computers may not be on at once. If you had one computer which was on all the time and had a large amount of storage you would have a number of options.
You could mount the users /home folder over the network.
A better option would be to set up rsync scripts that incrementally sync:
- on node login from server -> node
- on node logout from node -> server
You may also have to look at an app called Unison in the software centre but ive never used it and I think it could be quite old.