What rear axle to purchase and narrow

If you decide to go with a Ford 9 inch you can get stock disc brakes if you look for a 70s 80s Versailles and loaded Granadas and Monarchs.
I would not go that route and I have two of them (Versailles). Parts are hard to get for the disk setup

The correct answer is FORD 9 INCH. 3rd member, so it's easy to swap gears (even for an old man) tons of support and parts available, and "looks enough like" an 8 3/4 that you just don't need to say anything if you don't want to LOLOL

Beware in your travels, that you don't get a Ford 8-ish inch used in some of the smaller cars (looks just like a 9) or the Lincoln type 9" "plus" which looks like a 9, uses a different ring gear, and has LARGER than 4 1/2" bolt pattern

Ford Axle History and Identification: Ford Differentials

Here's some stuff on the "bigger" oddball Lincoln axles

How to identify 9 3/8 LS or open axle from the outside? - Ford Truck Enthusiasts Forums

You CAN, I am told, install a 9" 3rd member into a "big Lincoln" 9 3/8 housing. IF you are having custom axles made, one of those housings "cheap" might be an option