Transfer case uses the same ATF as the AW4 auto transmission. Do not use Dex III junk, GM does not license III anymore so anything that says III is "compatible" to the manufacturers profit point. Dex VI is the licensed formula and is backward compatible. Make sure you can get the top fill plug loose before you open the bottom drain plug. A screw-on nozzle makes it easy.
AW4 has a drain plug makes it super easy. I would not drop the pan unless ugly stuff comes out.
90w gear oil for the diffs (use additive if you have LSD). You need to pop the cover to drain them, then use the screw-on spout to fill through the drain hole. If you don't want to get into all that (and the gaskets and everything) then just pull the fill plug and stick your finger in the hole to see how the fluid looks.
Basic grease for the gun, nothing fancy or weird, you want to lube stuff not pack bearing