I think a lot will depend on how one plans on using it,
I you want a power down shift if it gets tough pulling then a automatic may be a good choice, but I would think you would want a manual transmission behind it for the basic gear/speed range, so the auto would normally run in high and the torque converter would not be slipping much,
at one time through racing outlets they made a clutch kit that would replace the torque converter, and then basically you have a power shift,
another thing most would want is a governor for the engine so you can hold it at one speed/ rpm. (some old gas combines used a belt driven Governor that would control the carburetor, and then a bar would be used to slow the engine down or a spring attached to the govern arm to create more Resistance for the Governor to work against)
IF I was going to make a PTO for some thing like your making I would probably do either a electric clutch or a belt clutch and drive it off the front of the engine, and then off that shaft the hydraulic pump,
IF you use a transfer case I would lock it in low range and leave it or use some thing Like I suggested in the other post and drive some combine final drives, with the differential,
My concern here is for safety, I know how kids are, (big kids some times are not much better), and they will want to drive a small tractor, and most people if related will give in, but if you have a tractor that can go 60+ mph, you have some real potential problems, and if there is a way of shifting it to high they will find it.
Personally I would opt for the manual transmission, unless I was mostly going to be using it for start and stop chores, such as building fence, the automatic would be great for loader work as well,
we have a old fork lift and parts are very rare for it, (1950's) and we have considered remaking it if we lose the engine, or transmission components, to use a automatic and then some type of drop box to power the differentials or use if we can find a combine hydrostatic and put in between the differentials and then belt drive off the motor, the fork lift is 4 wheel drive.
but regardless get geared lower (I would not want top end over 20mph),