Ok that looks pretty simple... I was expecting a shiat load of pieces to be welded on.
As for welding them parts to an axle I would use MIG... Make sure everything is grease and rust free and nothing but shiny metal to weld to and that goes for both the axles as well as the parts you plan on welding on. With this suggestion I recomend with any type of welding for best quality.
You can stick weld (arc) if you like but the weld quality would be much better with MIG in my opinion.
For welser spec... I suggest a 220v Mig that will go upto 180amp's... As for setting up your wire speed and amperage that will be up to trial and error if you are not familiar with the MIG welder... Some people crank the amperage full tilt and some like there wire speed slow as well... so what it comes down to is personal preference on wire speed and amperage.
Select the area you will be welding these pices to and tac weld them on and look carefully and measure 15 times if you need to to get them correctly aligned. Tac welds are much easier to cut off if you make a mistake in calculation.
Once you are happy with the measurements and what not... feel free to burn them parts on permanently.
If you do not feel confident in your welding skills feel free to ask a friend to weld them on. There is nothing wrong with asking for help in making your rig as solid and safe as possible.
Looks to me like a very simple and effective system for SPOA in the rear of your XJ to the Ford 8.8 axle.
Good luck with your build and I hope this helps you through...
Kelly