But can anybody recommend a good version control system to use with LaTeX, or a way to collaborate on documents in a large(ish) group?
LaTeX is plain text and whitespace-insensitive so it works really well with conventional software version control systems. It may be advantageous for organisation and navigation to split the text up by chapter / section, etc. It just makes it a bit easier to navigate and work with in the presence of many people changing things. That handles the tech side - now you just need good communication.