For what you want to do I think a 1 ton is more than strong enough (my choice) and the 3/4 would be fine if off roading was mild.
The 1 ton frame is simpler because it is straight other than the drop down starting at the rear of the engine, and the narrowing starting at about the transmission, from there back it's straight and parallel. A 3/4 ton frame is funny shaped for almost the entire length, slightly harder to work with.
I am sure you have seen this site, lots of good stuff for Cummins swaps.
http://www.4btswaps.com/forum/forumdisplay.php?f=2I have heard of, and I think talked to, someone around here who did the 3.9 in a 3800. John and Peggy know who he is, and may have even seen the truck. Apparently it's a pretty simple install.
Your truck will be pretty tall with 4X4, just to get the front axle to fit under the frame and still have some suspension travel.
Grigg