I used Valvoline synthetic 75w90 gear oil. I had no tags on either 'box or diff. I'm told you could also use a high-quality SAE 30 oil in the owner's manual.
I've heard really good things about Red Line gear oils, your open diff won't mind friction modifiers either. Since it's a track car you might want to swap out the diff rear cover for the Motorsport unit; it's finned with extra capacity and doesn't overheat & ooze oil like the stocker does.
So far both 'box and diff are quiet and shifting well. On other cars I've owned, the swap to synthetics may have increased my gas mileage slightly. It made cold-start shifts FAR easier, especially in below freezing weather.