I have more experience with ag trailers, and am now pulling a 5th wheel with a 2008 Dodge 2500 that has a 6.7L diesel engine and 6 speed automatic with both tow-haul and exhaust brake options. I don't know what conditions you will be facing, but it sounds like a lot of travelling so you will be seeing a lot of different situations. Trailer weight makes a difference going uphill where mileage will be much worse. And you won't make it all up going back down, where more weight will mean you need better brakes. And brakes are important along with gears to help hold you back in both automatic and standard transmissions. Diesel engines by themselves don't provide much braking, so some sort of exhaust brake would be very helpful in the mountains. On flat ground, as others have said, air resistance (mostly from the front profile of the trailer) has a bigger effect on mileage than weight. But you still need to stop. And keep in mind that speed makes a big difference in mileage - mine really starts to drop off, whether pulling or not, above 60 mph. I haven't driven enough with the travel trailer to say much about curves, but I expect this is where you will see the biggest benefit from a larger truck along with better brakes and handling in general. From reading in this forum, it sounds like there are also differences in handling between trailers of similar size.
If you are worried about mileage, cost must be a factor. Depreciation has been mentioned, and the difference in cost between new and used for both trailers (especially) and trucks is large. And, again from reading in this forum, new isn't always better, which adds something else to think about in an already complicated decision. Now getting back to your question, I get about 17 mpg in mixed daily driving and averaged about 13 pulling 4 horses and a large stock trailer on my longest trip from California to Wyoming and back. Most of this was on I80, and the load was probably lighter than many 5th wheel trailers. From what I see above, I should be happy about mileage. Whatever you get, enjoying your travels is most important.