Lots of good advice above. My 2 cents
3/4 ton minimum
with a towing package. The tow package has heavier brakes, suspension and trailer wiring already installed. 4WD is a very wise option to have too because a 2WD pickup pulling a camper out of a grassy area can get stuck in a heart beat.
Diesel is preferable. I also prefer either a mini-5th wheel or gooseneck for towing. It is much more maneuverable, better towing, and safer braking due to the positioning of the tongue weight slightly in front of, and over the rear axle instead of cantilevered behind it on a receiver hitch.
10K lbs behind a 6.0 Ford is totally doable. If you go with a used 6.0, there are a couple of things to do to bulletproof them; namely removing the EGR coolers and not tuning them up to high HP. Head studs are a good insurance policy too.
IMO, Dodge has the best engine (Cummins), Ford has the best chassis, and GM has the best transmission (Allison) if you're into the automatics. All of the various brand standard transmissions are ok too.
A larger gas engine will tow the weight just fine too, as long as you don't have too tall of an axle ratio, but it won't pull as easy as a diesel. Re axle ratio, 3:73 is probably the best compromise between towing power and fuel economy in the older vehicles. With the new ones with an 8 speed transmission, other options work well too.
When I sold my F450 I moved up to this (but it might be overkill for your needs!)