I don't think that using Git and Dropbox is the way to go... Just think about the features of both:
Git:
- Allows you to have a central repository
- Allows you to have your own repository with your own changes
- Allows you to send and receive changes from the central repository
- Allows multiple persons to change the same files and them merges them or asks you to merge them if it can't do it
- Has web and desktop clients to allow access to the central repository
Dropbox:
- Keeps everything in a central repository
- Allows you to have your own versions of the files in the server
- Forces you to send and receive changes from the central repository
- If multiple persons change the same files, the first file committed is replaced with later commits, and no merge occurs which is troublesome (and definitely its biggest disadvantage)
- Has web and desktop clients to allow access to the central repository.
And if you're worried with sharing some of your files, why not cipher them? And then you could get the biggest advantage of Dropbox to Git, that is, to have public and private files...