Sometimes snowbirds here in AZ sell truck and camper combos together, they can be a good deal. For all but the lightest of trailers you are going to want a 1 ton truck. If you get a huge camper you need duallies, 8 foot campers can get away with single rear wheel sometimes, 9-11 foot camper need dual rear wheels, all require 1 ton trucks. Even the mid size campers are going to need a 1 ton, don't bother with 3/4 ton, they cost the same anyways.
Pop up campers sometimes can be 1/2 ton, small campers can be 3/4 ton. Especially on the older trucks, the payloads are less than on the equivalently termed 3/4 and 1 ton newer trucks.
A lot of the Chevy 4x4 comes with lockers, look for that as it is a huge deal for off roading. Look for the G80 build code on the glove box, even some Z71 4x4s don't have lockers.
Check the loaded weights of the camper, they are much heavier than you would think.
Get a long bed, the gas mileage will be the same, but that extra 2 feet makes a big difference.