Upgrade then restore, or the other way around?
Apple's Migration Assistant does a great job at importing data from previous installations or backups. Therefore, I suggest you save yourself some time and do a clean install of the version of macOS you want to finally use and then use Migration Assistant to recover your Apps, profiles, etc.

As suggested by @SteveChambers:


back up
create a bootable USB installer or use internet recovery
reformat the drive
install macOS, 
restore from backup using Migration Assistant