What is the definitively correct way to hook up a 3-prong …
The "definitively correct way" is to run a ground wire to the socket location (which you can, without needing to follow or replace the present Hot, Hot Neutral wiring, since the 2014 code cycle IIRC) and toss that 3-wire socket in the trash and use a 4-wire cord to a 4-wire plug to a correctly wired 4-wire socket. –