Ford or Chevy class C , like a 24’ model with no slide would your best option to save weight as a tow vehicle.
That will offer you the most payload and tow capacity while giving you two full size sleeping areas. Ex: Sunseeker 2350 LE floorplan as i have.
You can tow a new pickup by flat towing it 4 wheels down or use a tow dolly. Both options might cost you $2-3k to buy and set up the right equipment to tow.
A dolly needs to be registered and inspected as well as maintenance such as tires, bearings, brakes etc.
I think most people that have done both prefer 4-down towing because there is hardly any hitch weight involved and you do not have to store a dolly. Towing 4 down requires a solid tow bar and hitch plate on the truck plus braking system and lights.
Chevy Colorado , GMC Canyon or Ford Ranger might all be able to be flat towed with automatic tranny and 4WD . Check with manufacturers to be sure. That list of vehicles can change from year to year, just verify to be sure.
If you choose to flat tow, unlock the steering column to the first click to free up the steering wheel because by turning to the second click ‘the run position’ will record mileage on the odometer.