Get the manufacturer's numbers for the dry weight and the maximum gross weight. The maximum gross weight is what you want to be able to tow and do so without being at 100% or near 100% of the vehicle's towing capacity.
Download the towing guides from Ford, Toyota, GM/Chevy, and Ram, and then look at which of their vehicles will be able to tow 120% of the maximum trailer weight. You will find that the towing capacity depends in part on the engine and to a great extent on the gears provided.
With a used vehicle you can do a lookup with the VIN to find out about how the truck was equipped at the factory (tow package, etc.) and the gears provided.
With GM for example the 4.10 gears provide 25% more towing capacity than the same vehicle with the same engine with 3.73 gears, which is important to know for towing a heavy trailer. The lower gears also enable the vehicle with its tow load to accelerate faster for merging with freeway traffic, better able to pull a steep grade, and shorten passing time when getting past a big rig pulling a heavy load at a low speed.
Most trailers fall into the under 8,000 lb. or over 12,000 lb. categories. For the second group you will want a diesel engine.