from my experiences with 1/2 ton pickup, 3/4 ton pickup, 2 Travel trailers, one approx 7500lbs catscaled , second 10k lbs cat scaled.
you will be waaaaay happier with 3/4 ton. gasser is fine. my current truck is a f250 6.2 gasser, i like to keep things simple.
payload on the truck is crucial.
you can spreadsheet numbers all day long and adjust what you payload but in the end i decided on a 3/4 ton when i had the first 7500lb TT after towing it for 4 months with my old f150. i was borderline overloaded each trip.
if you start shopping prices on new and used trucks, i know here in north carolina you can get 3/4 tons for the same prices as 1/2 tons
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always had great towing experiences