Royal Purple. It is expensive but it is not like engine oil. Don't have to change it quite as often. Might as well go with the better stuff.

 

what grade 5w50?

 

use 40 percent royal purple, and 60 percent honda fluid

 

I'm actually using Royal Purple's Max Gear 75W90 gear oil with no additives right now.. I don't have a Quaife, but it's still a mechanical based LSD, so it requires roughly the same weight.
I haven't had any issues out of it, but I'm going to be switching to Torco's RGO 80W90 gear oil in a few weeks. I was going to use their fully synthetic based gear oil (SGO), but they have an LSD kit that comes with 2 liters of the RGO and the Type F additive for $22.25, so I figured I'd try it out.

 

You can put in regular MTF in with a Quaife if you want. Whatever floats your boat, the diff doesn't demand anything special.