Restore Ubuntu 16.04 without losing files and settings

Solution 1:

Boot from a live DVD, mount your partitions and copy the files you need to backup to a USB disk or to google drive or something similar.

Your personal settings will be inside your /home/. Server settings though can be scattered all over the place. Hosting a website on that system? Have a database running?

The least risk next would be to re-install without formatting home or with "keeping your personal documents" by =replacing= your current Ubuntu.

It's absolutely vital for me to restore it without losing any file and most importantly any settings

Time to become very serious.

If that is vital to you I would claim you should have several tested backups and a restore plan for every personal file and setting I made in my system. Otherwise I claim you do not act like it is vital to you.