Rear fluid
I guess the 1st decision is whether to go synthetic or not. I have previously tended to go synthetic or all fluids, but have since concluded that I don't want it in the trans because it may be too slippery there, and I think U need some friction for the band surfaces to hold ? I think either will work in the rear, and I went ½ & ½ on my last fill just because that's what I had on hand. Come to think of it we also have clutches there in the Ltd Slip, so maybe U want some friction there also.
I have a new Eaton ready to go in (no hurry-that's another story), and I noticed that they said NOT to use synthetic. Maybe that's because of the limited slip ? For pure lubrication, like the engine, synthetic should definitely be better. Another thing, I think synthetic is more prone to leak.
So, I guess my conclusion is a good quality petroleum based fluid like Castrol, etc. and check the label to see if it passes the GL-5 test. One mechanic told me to get the specific GM additive rather than store brands, so I bought some from GM for ~ $5./bottle.