I don't plan on putting tires bigger than stock.
But what transmission would be a good choice with the set up of a 6bt with 4.88 gears?
Well it is a divorced transfercase so you can choose just about any 2WD trans out there within length considerations. What's the intended use of the vehicle? With 9.00-16 bias plys and without brake upgrades 80 mph highway cruising probably isn't the best idea so I'd assume you're shooting at more of a local area use truck that might see 65 mph top speeds.
I'd look for a 6BT setup with an OD trans out of a Dodge pickup. I'm not versed on what came in the Dodges so I can't point you to specific transmissions there. To keep it manual and 'old school', go the SAE housing route and use the Spicer 3053a, a 5 speed OD that was used in many deuces.
Keep in mind the NP200 is an offset rear output so it's always transmitting the power through gears internally, even in 2H. It makes for a noisy transfercase and thus running a big OD before it to get the speed up also increases the noise and heat. These transfercases can get too hot to touch with stock setups.
There are multiple reasons why many folks swap different axles front and rear into M715s. Stronger front, better brakes, centered rear for use with a different transfercase(like NP205 for example), gearing choices, wheel lug pattern, etc. However, with your plan of using the 9.00-16 tire size and my assumption of occasional 65 mph use vs 80 mph, you should be OK with the re-geared but otherwise stock setup.
36" tire, 4.88 r/p, .82 OD, 65 mph = ~2400 crank rpm
same setup but 80 mph = ~3000 rpm
The transfercase will 'see' higher rpm(~3000 rpm and ~3600 rpm respectively) and it will be very loud.
stock: 36" tire, 5.89 r/p, 65 mph = ~3600 rpm
80 mph = ~4400 rpm
Ken