How can I select the best platform for organizing a book?
If you're the only technically-literate person on a team of academics, I would eliminate the options with a learning curve.  Especially since academics tend to be quite resistant to change (well, most people are, but academics even more so) and you mentioned someone uses WordPad (yikes).

Yes, Git or Subversion or the many other collaboration tools out there would work great, but unless you're going to oversee the training of everyone AND they are motivated to change the way they work, it's destined to fail.  It takes practice to be good at these things.

I would recommend two steps:


Use Dropbox with extended version history that everyone can treat just like a drive on their computer
Split the various parts of the book up into many different files.  This way someone can open the file for chapter 1 and work on it while someone else works in chapter 13.


This way, if there ARE any mistakes, or someone edits someone else's work out of existence, Dropbox will handle version control in the background that allows for recovery.  And most importantly, your collaborators won't really need to change many habits for it to work.  Work in a format everyone knows, like Word, and deal with formatting like LaTeX later when the text is completed.