As I think you know, you have lots of choices here. Lets start by saying that your K member will support pretty much anything you want to put in, however if you were to go big block you would probably want to change out the torsion bars (you might want to regardless to improve handling and drivability).
As to which engine; You can go old school (318, 340, 360, 383, 400, 440), old/new school 5.9 (360) Magnum, or new school 5.7 Hemi. Each path has its advantages, issues and cost implications.
Old school - pretty straight forward, lots of support and knowledge online, huge after market, depending on the donor engine, its conditions, the options you choose, can be relatively inexpensive or very expensive.
Old/new school - much like "old school" its pretty straight forward. These engines are an improvement over the original LA engines in several ways not the least of which is the roller cam. That said, you can put a roller cam into anything, so there is that. The Magnum heads are reportedly better, but then you can buy new aluminum heads for old school engines where are as good or better.
New school - a few challenges here, specifically what transmission to use. You can use the old school trans (904 and 727) with an adapter plate so it isnt a huge issue unless you want to run really steep gears (4.10, 4.56, 4.88, etc), then you might want an overdrive. You can use a modern trans but you will have to cut the trans tunnel to make room for it. Another challenge here is the wiring, Mopar makes a stand alone harness to make this much easier, but you will have to mount the CPU some place.
Which ever path you choose, I would highly recommend going EFI. You can do so on any of the options to include old school. If you go with an aftermarket EFI system such as Fitech, its like 4 wires to hook up, if however you go with something like a Holley EFI, MSD, etc you will have to mount a CPU and run the harness. The benefits of EFI far outweigh the effort to install it; I ran carbs for many years and have or will convert every vehicle I have (5 vintage vehicles) to EFI. The other aspect of EFI that some don't like is that you need to install a commensurate fuel system; fortunately Tanks Inc. sells a bolt in tank and pump. You will need to run feed and return lines.
You can run a carb for sure, they have been used for many years and have served well. The down side traditionally is tuning and if you don't drive the vehicle frequently you can have issues getting the car started and running at times. Ethanol based fuel and carb gaskets don't get along, but if you can source Ethanol free fuel you can get past this easier.
As to cost, they all are pretty much the same depending on a wide variety of issues (where you start, where you want to go). Personally, I would recommend going with a newer Magnum engine at least, preferably from a running low mile vehicle. That said, if it were me I would go Gen III Hemi with a 904 or 727 trans (or better yet a manual). You can buy a brand new engine with a warranty for less than $5k, slightly used engine for $2500. the engine harness and CPU is like $1700 and lots of people have now done this so there is quite a lot of experience out there. There are some issues on which engine (year/model) to focus on which has to do with the accessory drives. The advantage here is that you get modern power, lots of parts available, modern reliability, etc. The next car I build (my 68 Cuda) will go this route.
Of course you can stay old school. The key here is to find a good donor engine. Do your homework and never take the seller's word as to what an engine is or what it represents. If the engine is purported to high speed and big HP, etc. get proof and try and find an engine you can hear run before buying. Keep in mind that if an engine is great, why is it being sold. Many people build engines with the wrong components that while they run are a nightmare (won't idle, low vacuum, lots of blow by, etc.). Try and get a guarantee if possible; can be difficult of course but at least try. Be very wary of the seller who says "I don't know anything about this engine".... those are code words for "this is probably a pile".
Look hard at remanufacturerd engines, check your local O'Reillys or Autozone, you might be surprised at what you will find. You can buy a "reman" long block 5.9 360 from a 89-90 Ram 150 (1500) for like $2K; perhaps throw a cam in it (for fun), intake, valve covers, cam cover, oil pan, accessories, exhaust and you are there. You can probably find a short block as well and then go with some aftermarket heads if you are feeling froggy..
you get a warranty and don't have to wait on the machine shop.
This brings me to the next option, visit your local machine shops and see what they have. Every machine shop I have ever been in has a number of donor engines laying about. You might be able to score a deal.
Given your stated minimal experience with building an engine, I would recommend you stay away from engines laying in people's yards that seem like a great deal. Again, if the engine was a stump puller, high HP motor it wouldn't be laying in a yard. Of course they will all say "it ran when pulled", well in my experience that usually means "it was broken and we had to change it". Last engine I got like that had 4 bad cylinders with the piston ring lands completely broken yet the previous owner swore it "ran great".... Now, if the seller can start the engine for you, then I might entertain it if I needed something to drop in. Of course the best case scenario is to hear the engine running in a vehicle, actually drive it and access it. Do not forget to pull the dipstick and check the oil. If it is very clean, it could indicate that there is an issue he doesnt want you to see (as in a leaking/blown head gasket); no one changes the oil to sell an engine. Also look at the exhaust and see whats coming out; have someone rev it while you are behind it and listen to it, smell it and watch it. If you have the capability and intend to merely drop it in, you would be well advised to do a compression and a leak down test on it (or have someone do it for you).
Regardless of what you do, do not hesitate to post on here any questions you may have. We are happy to help.