As a Firefox on Linux user I checked one of those sites that tries to estimate how many bits each public aspect of your setup reveals about you. It turned out available fonts was by far the most unique aspect of my setup.
http://yinzhicao.org/TrackingFree/crossbrowsertracking_NDSS1...
Use Tor Browser even if your not using Tor if you're looking for better privacy. It's modified to mitigate as much as possible. Facebook is just bad. Avoid it at all costs if you value privacy. And it's not just facebook. Sites like facebook, google, etc also use several 3rd party "advertising" (i.e. data gathering) companies to gather data and build profiles on users and share that data with each other. Even on your regular use browser I would highly recommend uBlock Origin and Privacy Badger.
Total is around 20bits (due to overlaps).
YMMV.