If you have stock adjustable tapered wheel bearings on your axles you need to have the thrust plug (button) installed in the middle of the diff. If you have aftermarket sealed ball type axle bearings (commonly referred to as green bearings, non adjustable) you do not. There is much debate on whether greens are OK to run on the street. My personal opinion is that factory style tapered rollers are superior. If you have tapered rollers you will need to read up on axle adjustments.
If the u joint is a different size you will need to order a "conversion" joint. They are commonly available. Do not intermix the u joint retaining straps between the small (7260) and large (7290) joints. They appear very similar and can be confused but are dimensionally different.
Checking backlash and pattern can be done now, however if the used gearset has been run for any length of time with a bad pattern and backlash it will be worn and will always be noisy even if you try to correct it. If the backlash is ballpark you should just leave the adjustments alone. Do check that the pinion nut is tight.
This is a prime time to check the sure grip clutches. They could be worn out and it may act as an open differential. They can be replaced. Also prime time to service the rear brakes and axle seals.
Your speedo will read all wrong with the new gears. If it bothers you the drive gear in the transmission will need to be changed.
There is also some debate on if you need to run a gasket between the third member and housing. Again my opinion is that it should be there as it spaces the third member slightly forward for proper axle alignment.
All of the above procedures are in the FSM. Dr. Diff is a good source of parts and info.
Good luck and have fun. The difference with 3:91s will blow your mind.
