Any SUV will work but my first choice would be a Toyota 4Runner which has the same frame as the Toyota pickups. Most SUV's have a body that is common to passenger cars. For example the Toyota Highlander shares the structure of the Camry sedan.
ALL the manufacturers have towing guides that you can download in minutes and check the recommendations as to tow load. If a trailer fully loaded is at 50% of the maximum I would be OK with it. Over that and more care is required in making the selection.
Something to consider is that a crew cab pickup truck, even a mini truck will seat 4 inside and have a small box/bed area that is available for hauling bicycles, etc. or with a fiberglass cap/shell you can add a rack for skis and kayaks.
I think that a pickup truck pulling a travel trailer provides the most versatility of any RV setup.