Get a F350. Make it a Chevy 3500, if you want a smoother ride while empty (personally, I couldn't stomach the Chevy's square wheel-wells).
I went from the base, factory, 17" steel wheels and All-Season tires to 18" aftermarket wheels. The new tires are about 1/2"-1" taller and a bit wider, with more capacity (3,638 pounds per tire). I believe my new wheels (3,500 pounds per wheel) are rated higher than the factory steelies, too. I planned it that way, because I knew I wanted custom wheels when I ordered the truck. My speedometer read fast with the factory set-up and is accurate with the taller tires (according to GPS). My Carrying Capacity Rating (2,983 pounds) may have been slightly lowered, due to the factory steelies and SUV tires, but I'm not certain of that because it seems the F250 is limited to 10,000 pounds, no matter what. As far as gas mileage goes, that's only going to be as accurate as your odometer/speedometer. For me, anything over 55 mph starts cutting into the mileage at about 1% per mile a hour, to a low of 8.5 mpg at about 68 mph while pulling the trailer, too. If I see 10-10.5 mpg without the trailer, I'm pretty happy, but that isn't happening at 65 mph.
I have a 2013 F250, gas, 4x4 extended cab, 8' box, 4.30 gear ratio with camper package, 10,000 pound GVWR. It has power windows, locks, mirrors, etc., which lowers the CC rating. The suspension is the same as a F350, but the F350 has taller axle blocks, permitting the truck to sit more level with a load. The spline count on the drive shaft is different on a F350, too. I think the brakes are only different on diesels.
I saved a few bucks getting the F250, including the mild suspension mods I've installed (which are often installed by F350 owners, anyway), and it handles our 3,000+ pound camper while pulling a 3,500 pound trailer, but if I were to do it over, I'd get the F350. If, for no other reason than the peace of mind from simply keeping the truck within bounds of liability regarding the Carrying Capacity Rating.
Your salesperson should have access to a chart or factory contact that can define the difference in weight ratings amoung various wheel/tire combos. Any info I've presented should probably be verified by your salesperson, too. Some of the New Car sales staff may or may not be Super Duty truck-ordering specialists. There are a few ins and outs to consider.
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