Your trailer will be at home behind a half ton no problem and any of the big engine half tons with towing gears will tow it and stop it virtually the same as a 3/4 ton.
I don’t have the same payload sticker paranoia that some do though.
The 3/4 ton gasser will be more stable and slightly better brakes. (Yes if you opt for really deep gears it’ll pull better too, but so would a diesel or semi tractor. Where do you stop?)
Is a F250 overkill? I dont think so. I prefer HD pickups. Is a new well equipped half ton out of its league? No it’s not.
Think duty cycle too. What’s the split? 300 days commuting and 50 days towing or the other way around?