The transfer case doesn't really come into play. It just hangs on the back of the tranny.

In my opinion, you will need a true tranny jack, from a rental yard. I would get a 1000 lb. rated one. The tranny/tcase isn't that heavy but you need the reach of a big tranny jack, particularly since you will have the rig on jack stands, preferrably the six ton truck size.

Also, don't try to save a few bucks by not draining the tcase and tranny.
Basically, you remove The shifters and the various shields, remove two drive shafts (rather than one on a 2WD), remove the middle portions of the exhaust system, then upbolt the tranny from the engine. The top bellhousing bolts can be a pain to get out, but a 24" and a 12" extension, or better yet, a 36" extension make it doable. You will also need to disconnect 1 or more switches, depending on the options you have. You will also need to disconnect the clutch slave cylinder.

A trick I learned from Curtis Johnson is to run a short ratchet strap around the tranny and then connect a large ratchet strap to the the first strap and the other end around your rear axle and then crank on the ratchet. The tranny will pop right loose if everything is disconnected.

I have had mine in several times in the last couple of years and I have made most every mistake I can think of.