I would also sitck with a mid-80s CJ-7 (in fact, I did!). In terms of finding a stock, or near-stock unit, ie. one that has not yet been built up, a few rare '86 CJ-7s came with a Dana 44 rear axle - this is good. You can tell because the AMC model 20 is round, the Dana is not.
Most of the stock trannies, T-4, T-5, and the other 4 speeds (forgot the #s) are not very strong, but unless you add a powerfull motor and tires over about 33", a well rebuilt tranny is OK, as you said you will only go off-road occasionally.
I would likely never buy a jeep with a 4-banger, even though these are decent 4-cylinder engines, the 6 wins hands-down. Like others have said, fuel injection does wonders (I have the MOPAR kit).
Just watch out for home-made crap and conversions. If you do not know what you are doing (you didn't say) it can be hard to tell if that Chevy 350 and other swapped-in stuff was done right. But, stock CJ's are dissapearing faster than Taliban idiots.
Good luck, and feel free to scan Ebay for a "feel" of what is (supposedly) out there.
'82 Scrambler - NV4500/4.5" lift/33" Toyo MTs/4.0/twin stick, and my windshield washers work! Full 1/2 cab Cage
2004 Grand Limited 4.7 HO - OH Boy!
2010 Grand Laredo 5.7 Hemi - SICK - work vehicle -gone - replaced by an 08 Tahoe - nice ride.
"Both my Doberman and my Jeep can accurately be described as 'black and rust.'"
"I got a fever . . . and the only prescription is more cowbell"