Using "LS" to refer to the overall platform of Gen III and Gen IV GM motors is such a common colloquialism that GM might as well start calling it that
Anyways, I can chime in here too since I have some Magnum experience (with some Hemi experience coming up quick!)...
The Magnum is a good swap candidate for many reasons that have already been pointed out: good power gains that respond fairly well to simple upgrades, reliable, easy to wire, works with factory gauges, works with factory fuel system, can use factory AX15 (though yours is an AX5), etc. I've built a handful and am currently rocking a ~500hp/575tq 408 Magnum in my 1993 RamCharger (which I'm also currently building - because nothing makes the Mrs. happier than two shitbox projects
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On paper, few would say that the 5.2L is "worth it" for a swap candidate. The numbers simply aren't that impressive. However, any one who's driven a 4.0L and a 5.2L ZJ will quickly confirm that the driving experience is quite different between the two. The 5.2L makes power down low, has a nice wide torque curve and generally makes for a spirited driving experience. The 5.9L improves upon that, shifting torque down even lower in the RPM range and (in factory form) adding a bit of stall speed to the converter to make it much more fun on the street.
If budget is a concern, the Magnum wins. I picked up a running and driving Ram 1500 for $550. I took the engine, trans, t-case, harness, and ECM then flipped the chassis and made a good bit of $$ (that wasn't my intent of course, but certainly a nice benefit). I've picked up a handful of running Magnums for cheap - the complete 5.2L I put in my W150 was $400 and I got to drive the truck before stripping it apart. Keeping the EFI (so I had to buy a later year gas tank and fuel pump) and I was into that engine swap for a whopping $800. Oddly enough, this truck was the one I traded for my current TJ (I had gotten the RamCharger after the W150 after decided I wanted enclosed cargo space). The guy drove it all the way from AZ back to WI getting 16 mpg the entire time and is amazed at how smooth it starts and runs (all stock, except I adjusted fuel sync to +4 which seems to work best with ethanol-spiked gas).
My recommendations on any junkyard swap is to of course fix the plenum and while you're in there, check the cam lobes. There are some mods you can do to help the factory Kegger intake manifold perform better (Check out UTAwesome Performance) as well as two "RV" cams that really wake these engines up (the Hughes version requires new valve springs which are fairly cheap). Freshen up the heads (at least valve stem seals) and add a Fel-Pro SD series head gasket and you're good to go for considerably more power at lower RPM's than your current setup.
For the transmission, you'll have to do some thinking. Now's the time to convert to an auto if you're rock crawling (or intend to). Note that any Dodge transmission or the AX15 with the Dakota bellhousing will require you to move the starter to the driver-side. This can cause some packaging issues with headers and manifolds, so sticking to a set of center dump shorties isn't a bad idea.
Now that said, I've swapped and built enough Magnums to be happy with my experience. I'm also on my 5th 4.0L and quite simply - I have had enough... It's a good motor, but at the end of the day it belongs in a tractor. I know that isn't a popular opinion since many hold the 4.0L on some sacrilegious pedestal, but it's true. I've picked up a 2012 5.7L Hemi with 65RFE for the TJ - it's time for a proper amount of horsepower