Based on my experience, without an added cooler, the trans temp will hover around 100 degrees above the ambient air temperature, whether stopped or moving. So your max temperature is highly dependent on your climate.
With an external cooler (factory or aftermarket) the temperature will be lower, but it will fluctuate more. When the vehicle isn't moving and the radiator fan is off, the temp will creep up. The fan will cool it some, and moving will cool it more.
One thing to keep in mind when deciding what temperature you don't want to exceed is the location of the temperature sending unit. If I recall correctly, it is measuring the temperature after the fluid has returned from the cooling system. The temperature of the fluid leaving the transmission is going to be somewhat hotter.
Hills and towing will absolutely put a greater load on the transmission and generate more heat. Personally, if I were towing anything more than a small utility trailer, I'd want at least a small cooler in front of the AC condenser. If I were regularly towing a few tons, I'd want a large cooler. I added one myself and I have not noticed any decrease in AC effectiveness or increase in engine temperatures.