Selective file sharing remote and local between multiple computers

Question

I would like to set up some kind of a network that can achieve selective file syncing across a number of devices ie home computer, laptop, tablet and android phone, either over a local network or over the internet when available.

What I would like to be able to achieve is like the following:

Have a folder with subfolders on a home computer that is the main source.

Have other devices that sync certain folders depending on their specific permissions and configuration to those of the home computer, and vice versa where applicable.

Example: laptop The laptop and home computers have equal rights to sync a certain group of files ie, music, videos, documents. If a file is added or removed on the home computer, this will also happen on the laptop, and vice versa.

The laptop and home computers have unequal rights to sync a certain group of files ie, downloads. The laptop has rights to add files to the downloads folder, and the home computer will sync these, but if the laptop deletes files in this folder, they are not deleted from the home computer. Similarly, if files are added to the home computer's downloads folder, they are synced on the laptop until deleted.

Example: android phone Android phone syncs with a specific folder on home pc ie "phone music", where only files in this folder will be added to the phones folder.

Another example is downloaded files, whereby downloaded files on the phone will be shared with the home computer, but not vice versa, similar to the laptop example above.

I am not looking for a full walkthrough on how to achieve this, but rather an idea with where to start. I think that I would like to make the home computer a server running Ubuntu or the like, so that I can allow remote syncing - ie if my laptop is connected to the internet at work, and this is an allowed network for syncing, it would occur, and then also if it's connected to the local network.