That's a very big question you're asking there, Arend! More than I can really deal with in this post...It's something you need to read up on separately.
I will say two things though - firstly I really cannot imagine working without a version control system, although I did used to do so many years ago. Now it seems as crazy a riding a motorbike with no helmet or armour...whilst drunk.
I would also say that Git is not necessarily the version control system to choose, SVN (Subversion) is certainly easier to learn. There's a good response on stackoverflow to the question "Why is Git better than Subversion?" that, despite being written a few years ago, is still spot-on (ignore the other responses though they are very out of date).
I was really asking more so that I could answer your question with an understanding of how you work.
Anyway, in terms of sharing the files, you could just share the src folder plus the various files that sit alongside it (adapt.json, config.js, Gruntfile.js etc.) you could share the build folder as well but since that's entirely generated from the src you don't need to
I wouldn't try sharing the node_modules folder, you'll find it's really hard to move around (or zip up). If you pass the source files to someone else they can run npm install to generate their own copy of node_modules.