Expect the gasoline engines to pull 10,000 lbs well into the mountains but with some noise. If you plan to tow more through the mountains, get a diesel.
The F250/2500 is a good bumper pull truck, but you should consider the F350/3500 if you want to pull a fifth wheel later. Typically the frame and axles are almost the same but softer springs and lower rated wheels on the 3/4 class trucks.
You will need a weight distribution hitch and possibly sway control based on the the profile height of the trailer and trailer tongue weight bias.