Hi OldCityCat
Typical solution would be as follow:
1- install the old environment on a separate server (SQL 2012 and Dynamics GP 2013) , also create the ARC company from the GP utilities and restore your backup on it.
2- Upgrade the SQL to 2016
3- Upgrade GP 2013 to GP 2016
4- take a backup from the ARC company
5- Go to the live server and Create the ARC Company from GP utilities
6- restore the backup taken from the upgraded environment to the live environment.
The thing is you must upgrade the Company Database from the Dynamics GP 2013 to GP 2016, if you restored it without upgrading it wont work and will generate errors.
Thanks and Regards,