Pickup a shim kit, and a something to measure them with. Quite often in the process of pulling the bearings off the shims get damaged. Having a set on hand will save some time. Where are you getting the puller? I've been looking for a god set with the spacers/center buttons and everything so I don't have to borrow the one from work all the time. Bought the Princess Auto one but it wasn't big enough, DOH! Get out the price on an install kit, it will come with more stuff than you'll need but will have all the seals, bearings and shims that you'll need. But before spending a dime crack the cover and confirm they problem and make sure none of the gears are stripped,chipped,broken. Also check to make sure the front and rear diff ratios match, could be either 3.55 or 3.73. My sister bought her '93 ZJ at teh auction and got hosed! When we got it home we found out there was no front driveshaft! So we bought one and installed it but then there was a terrible banging from underneath. Pulled the front cover and found the teeth all file sharp! So I figured bad gear setup, bought another diff, put it in and had the same problem! Turned out that the front had 3.73s and the rear had 3.55s! Someone had replace one of the diffs and not matched the ratios! Fortunatly I had a set of 3.73 gears for a d35 in my useless to me parts pile. So I installed those and then FINALLY it was a driveable rig. Moral of the story, don't let family go to the auction alone, it will cost you way more time in the end! And confirm gear ratios front and rear before replacing a diff on a newly purchased vehicle!
As for your trannies, not sure what to suggest, my as well pull that oan and see whats in there.