37 to 40 ft and full time? You want a one ton and may well need a dually. I have 3500 CC SB SRW CTD pulling a 12,500 FW and a 2,700 lb utility trailer so a total of about 15,200 and 64 ft long. My trucks payload is about 3,900 and between the pin weight, pullrite sliding hitch, 3000 Honda etc I'm carrying about 3,500.
If all 15,200 was in a FW I'm guessing my SRW would be about maxed out and I'd then need a dually. My truck is 4x4 with 3:42 gears so I run in 5th gear. When not towing I can get 22.x mpg with it.
I use a pullrite 18,000 super slide hitch with a short bed because my older FW is a flat front and 102" wide. Some people do get by with a short bed and no slider but have newer FW with rounded corners and are very careful.
I mounted my remote start Honda 3000 at front of truck bed and run an 8 gauge cord back to a transfer switch. I also made the cord long enough so that I can park hood to pin and not hear the generator inside FW. I have a 2000 prowatt inverter for my 40 in led television, residential frig and other gadgets. I still run the generator to power the ac, micro, hairdryer. At times I will use the inverter to make toast.
I run six GC2 batteries and 1000 watts of solar panels. In the dead of winter running the house furnace, several hours of television, satellite, led lights, fan, laptops etc it's always charged up. Tilted panels of course.
When shopping for a truck pay attention to tire sizes, payload, axle ratio, and transmission model. They gave very good advice up above, learn all you can and shop slowly. You are in the top range of towing so dont let rv dealers convince you that a 3/4 is good enough. In my opinion anyway.
You might tow with a 3/4 if you found an ultra light 36' and dont carry much. My son is pulling a 35' FW bunk @ about 10,400 and his 2140 lb pay load/pin weight is maxed out. 2012 Ram 2500 CTD CC 4x4 long bed. He says it pulls better than his 26 ft TT did but for the size that is a light FW. He could pull more but has run out of pin which is common for a 3/4 ton. Good luck to you and see you in the desert. :)