For your browser bookmarks you want to back up I will suggest the add-on Xmarks
https://www.xmarks.com/ which will sync your bookmarks with their servers and between Firefox, Google-chrome,etc. and works on Windows, Linux and Mac OS, you will have to create an account but it is free.
Also Firefox and Google-chrome also offer their own bookmarks, password, add-on and theme synchronization.
May I also suggest installing on all your web browser the password manager LastPass
https://lastpass.com/ which will sync your password between all your computer and web browser
If it is your file browser bookmarks like for Thunar, Nautilus etc. you should look in your home directory for a hidden file named .gtk-bookmarks just do ctrl h to unhide the hidden files and ctrl h to hide them again.
Hoping this was helpful, good luck.