Alternative to Samba, maybe local cloud computing?

I'm looking for an easy, quick way for people to share files on our local network, ideally enabling multiple people to work on the same document, similar to google docs.

I have a dedicated Ubuntu server running Samba, but the permission structure often gets in the way of letting users organically make, edit, transfer, and delete files on the go. I've tried a lot of different permission settings, but it seems the more "convenient" I try to configure the system, the less secure it becomes, and every now and then files still get created as, or changed to read-only for no apparent reason.

I wonder what kind of alternatives are out there to enable more effective collaboration and easier access to local files. Any ideas?

Edit, Update, More Info:

We are a small non profit, located in a very rural area. Our internet connection is not reliable and we create a lot of internal data. The computers in our network run a mix of different Linux distros, also Win8, WinXP, and OSX.

We have seasonal interns so we have to be able to easily integrate additional computers and users with widely varying IT skills into our network. We use google docs for some things, but we want something that doesn't tax our marginal internet connection and still helps us simplify and organize file sharing and project collaboration across the local network.