I noticed the CJ Pony item your link goes to is an 8" third member and also a Traction-Loc. If your car is a Mach 1 it should have a 9 inch rear axle. The 9 inch rear axle was standard on 351W motor Mustangs and the 351W was the smallest motor available in a 1969 Mach 1.
So, I am assuming you have a standard 9" ford rear axle and it's not a Nodular Case third member nor have a Daytona Pinion Housing or be any type of Traction-Loc. Basically you need a Ring and Pinion Gear set of your choice, and an installation kit like the one below.
Installation kit:
https://www.summitracing.com/parts/mgr-r9rmkt/overview/
If you have an existing Traction-Loc posi traction unit or are purchasing a new one it needs specific ring gear bolts. They have a smaller hex size, 5/8" instead of 3/4", to fit into a counter bore. There are also long and short bolts. I don't know what determines the length but I have always needed the longer bolts.
Bolts:
https://www.summitracing.com/parts/rat-1305/overview/
Typical Traction-Loc unit for 28 spline axles. A unit for 31 spline axles would only be needed if a previous owner upgraded to 31 spline axles. 28 Spline axles were standard on 351W based cars.
https://www.summitracing.com/parts/fms-m.../overview/
Installation kits come with a pinion bearing preload crush sleeve. If you desire, you can opt for a solid pinion spacer instead of a crush sleeve. They take more time to setup the pinion bearing preload. But, do a better at maintaining the bearing preload.
https://www.summitracing.com/parts/rmg-0.../overview/
I would stay away from Richmond brand gears. Richmond also has a lower end line. I don't recall the brand but I would avoid those as well. Richmond gears tend to be noisy. I have had good luck with Motive's Performance series. I think Mustangmike had good luck with US Gear. Yukon gear is also supposed to be a good brand.
If you can follow instructions and have some basic mechanical skills you can setup a 9" rear axle. Some tools are needed that you might already have.
1) Dial indicator to measure backlash,
2) Inch pounds bar type torque wrench or dial type torque meter to check bearing preloads by measuring the torque needed to rotate the pinion gear at the pinion nut.
3) Pinion depth measuring tool or depth micrometer helps to set the pinion depth instead of the trial and error method.
4) 1/2 inch drive foot pounds torque wrench
Mike