I'd look at a truck's actual payload capacity and a TT's actual tongue wt. before you look at choosing a stronger receiver.
With all the options you want on the F250, the actual payload capacity could be a lot lower than what you expect. Ours with 4WD, supercab, long box and a canopy is down to 1800 lbs because of the added weight. If you want to be able to have passengers and cargo in the truck, the tongue weight of a 36-38' TT *could* possibly be too much without overloading the truck. Don't go by what the door pillar sticker or literature says for payload cap. And don't go by the advertised dry tongue wt. of a TT to make a buying decision. Tongue wt. can go up substantially, and in some cases, nearly double (like ours).
The longer wheelbase of a supercab (or crewcab) and long box sure is nice and would be better for a longer TT. Unless you really need it, I would not bother with 4WD because it's a big weight penalty plus the truck is higher off the ground. Or go to a 1 ton. I see people saying a lot that they are only a few more $$ anyway.
Maybe for another thread, but FWIW, if you get a crewcab and a long box, you may find that towing a long TT of 36-38' will be a handful for getting around corners, especially on city streets. With only a 29' TT, our F250 with supercab and long box can be "fun" to get around tighter corners sometimes. I find I have to get some turns set up right before entering it otherwise I can brush the tires on the curb or end up over the curb. But, to me a truck is not a truck unless it has a long box. We make use of the full 8' a lot.
