Stock gears should be 4.36 or 4.62 in your truck.
For t-cases it depends on the applacation. If your going to use a chevy tranny then you might as well use a chevy front axle (cheapest, parts truck swap) then I'd advise a chevy np241 with the shifter. If your going too run a ford,dodge or stock nissan front parts you could run a dodge version of the same t-case or a np205.
As far as a 3.0 vs 3.3 vs 4.3 swaps. The 3.0 is the cheapest, followed by the 3.3 swap then the 4.3. A 3.0 or 3.3 with the stock 5 speed and a 3.92:1 t-case gear set would crawl pretty good in 4low and would be easier to complete. But the 4.3 offers more power (yah the 3.3 sc makes power) then the 3.0 and build tourqe at a lower rpm.
For 35-37 inch tires you will need too do a SAS (plus no buddy makes a 6 inch lift for these trucks) The rear axle is good enough stock for this range of tires, although ifyou start making decent power (above 300lbs) or you stuff the rear into cracks you may want to switch to a 9 inch or dana 60 rear. Gearing should be around 4.88-5.13 with the 4.3/ 33s/c and 5.13 minimum with the 3.0. A dana 44 minimum for the front axle, a 60 is really heavy and over kill for your app.
But the first thing you should do is put the 3inch body lift on it and buy a used set of 33s. Just to see if you want too deal with a lifted truck day to day. And decode your axle gearing, on the passanger side of the engine compartent there should be a tag on the fender, it will ethier have HG43 or HG46 for the code, HG43 is 4.36 and HG46 is 4.63.