If you are "on the cheap", You don't want to use the 4L80E. Besides the fact that a stock 6BT makes more torque than the rated input torque for a 4L80E, you will need to buy the adapter plate (either aftermarket or settle on the "bread van" adapter) wave ring, flywheel and a few other hard parts.
Assuming you scrounge a "bread van" adapter bits (which will result in the engine being canted towards the passenger side and you probably won't find for less than 400 bucks), you will still need a stand alone controller for the 80E. That's going to cost you 500 bucks by itself. The PCM in the truck now will not run the transmission stand alone. It will be missing too many inputs.
You're up to 900-1000 bucks for just the "bread van" adapter and a transmission controller. You haven't even gotten the flywheel, wave rings, engine mounts, etc yet.
Cheapest way out is to take the complete drivetrain out of the dodge and drop it all into the Chev chassis. Engine, transmission and transfer case. You have all the parts in the dodge truck you need. You'll just have to build some bracket/crossmembers and have some driveshafts made.
Be aware that most people have interference issues with the IFS and the 6BT. they usually end up installing a cowl hood, suspension drop or grinding on the engine oil pan rail. Most say you need a body lift, but I know a few guys who got away without one by judicious use of the BFH and some form of bulge/cowl hood.
You're also going to run into issues with gauges, fuel system, exhaust and such but that's another thread for another day.
Cheap is a relative term. Assuming you just drop the dodge drivetrain in and can do your own fabrication, you're still going to have a couple grand into the final product.
It's going to take many many years to make up that amount in fuel savings. 3-5 grand buys a lot of fuel......
Personally, if the only reason you want to do this is fuel mileage, I would recommend you don't do it.
With older trucks like these, guys do this kind of work and usually end up getting rid of it before they even break even on the conversion costs.
Just drive it or sell it for something better on fuel would be my recommendation.
If you truly plan to keep it for another 5-10 years, it might be worth your while to do it.
Just so you know I'm not just trying to discourage you from it, I will probably be dropping a 6bt into my 98 6.5 TD if it ever dies again. BUt I'm after more than just mpg.
I tow.
HEAVY....