Will the tow vehicle be a daily driver, or only for towing?
How many people and pets need to be in the vehicle?
For many, a full size pickup offers open bed storage for generators and gas, while still having room for occupants inside the cab.
Others prefer a larger SUV (Suburban-ish), but that does beg the question on where gas and a generator will be during travel.
Smaller families can also consider the diesel midsize SUVs such as VW and Jeep GC.
Do you know the specs on your trailer? What is the tongue weight, dry weight, cargo capacity, and loaded weight?
Also do some reading on the definitions on payload and towing. It is an important calculation and often swept under the rug by automakers' sales messages. It is an independent calculation from towing capacity and may help you decide.