No one here knows exactly what data you have and where it is.
But a "best guess" is... back up your home directory. (Desktop, Documents, Downloads, Music, Pictures, Videos) and that should catch most of it. (Unless you store your files in a non-standard location).
Also keep in mind.... most (but not all) your data (word processor files, spreadsheets, pictures, mp3s, etc..) will work in Linux, but not all of them, not 100% are guaranteed to be compatible.
You aren't going to be able to not lose your data, if you get rid of Windows and replace with Linux. Both OSes use different file system formats. So you will have to wipe out everything on your hard drive to uninstall Windows. So my suggestion is to get a USB drive and save all your data that you don't want to lose onto it. Then do your installation to your hard drive, replacing Windows with Linux. But like arochester says, the best thing to do is to dual boot till you have everything setup on Linux. That way if something goes wrong you can always get back to where you started, in Windows.
Another option is to phisically remove your windows harddrive and install linux on a different harddrive.Put the windows drive on a shelf somewhere in case you want it again.When you are sure you dont need winows anymore,use it for backup in an external case.This avoids any dual boot issues you may encounter.