I like to have a good backup from my small debian server.
Would it be a good idea to make a repository at "/"?
Not really. There are a lot of continually changing files under directories like /var/log that are not suited to using a version control tool. Also, files under /dev and /proc are not regular files and can't really be versioned in the way a VC tool would expect them too.
Backup software is a much better fit for what you're after, probably something like: tarsnap; backula or a similar package.
Git isn't a back up tool, no version control system is a substitute for a backup tool. The don't conceptually serve the same purpose, and don't functionally either. Not to mention that there are directories that constantly change and symlinks and other file-like things that aren't really files that a version control tool wouldn't even begin to understand what to do with them.
If you want to version your entire partition so that you can edit config files and such willy nilly and revert changes, you could do that with a very extensive and complex