What I'd do (short version):
1. Get an external drive large enough to hold the contents of your internal drive.
2. Use either CarbonCopyCloner or SuperDuper (DO NOT use time machine) to create a bootable clone of the internal drive.
3. DO A TEST BOOT, just to be sure.
4. Now, boot to internet recovery:
Command-OPTION-R
5. Once the utilities load, open disk utility.
6. Go to the view menu and choose "show all devices" VERY IMPORTANT
7. In the list on the left, choose the topmost line (physical drive) and erase it to APFS with GUID partition format.
8. Quit disk utility and open the OS installer
9. Start clicking through. The Mac will restart one or more times, and the screen may go black for a few minutes with no progress bar. BE PATIENT.
10. Once the install is done, you'll see the initial startup screen (choose your language).
11. Start clicking through. At the appropriate moment, setup assistant will ask if you wish to migrate from another drive. YES, you want to do this.
12. Connect the backup and give setup assistant time to digest everything.
13. I suggest you migrate everything. Again, give the migration time to complete.
14. When done, you should see you old login screen. Log in and "look around".