I'd see if you can get that 5.3 Vortec engine!
You can most definitely mount an older transmission to it, if you feel the need
TH400 would be the easiest in that aspect as well, as they don't need a kickdown cable like the rest of the transmissions do.
Personally, I'd get that 5.3, all the wiring, and electronics, then buy a 4l60e for the truck. The 5.3's computer will control the transmission. If you can get the whole truck cheaply, then yeah, you can get that 5.3 installed fairly cheaply too. You will need to get the PCM flashed, and that does cost a few hundred at this point in time. But as far as I am concerned, its well worth the effort