If you travel with two 100# labs and 80# of dog food you are going to be 280#'s heavier than the the guy who doesn't. Everything is weight.
This is how to determine what you will have. Im not saying payload is law but you asked about payload .
Your tire ,wheel and axle rating is the important number,especially the rear where you will be carrying most of the weight.
This is just an example:
The average 350 DRW is about 8000# on a scale (depending on engine choice and dealer options). Add whatever you normally would carry inside the truck on a trip, your personal options. ( Tools, dogs, people, front hitches and cargo boxes,fishing coolers)
ADD the weight of aftermarket goodies , tie-downs, super springs, stable loads,air bags, timbrens, sway bars, super hitches.... now your truck is 9000# before you think about adding on a camper.
Example: take the truck to scale and weigh it, thats the only way to to really know what YOUR specific truck weighs. Take the trucks GVWR and subtract what your individual truck will weigh.
Once you determine that , you will have a payload of ????# probably less than you expected.
PART 2.
When you pick out a camper, take into consideration the weight of water, extra batteries, solar panels, generators, propane, food, clothing, pots,pans, dishes, silverwear, chairs etc, etc, when you add all this stuff to the 'DRY WEIGHT' of a camper , expect 1000# - 1500# plus of added weight.
My camper is 1500# over the MFG. posted dry weight and i have a SB camper with no storage . Posted dry weights on campers do not include camper options. A real number would be the shipping weight after its all built and ready to roll out the factory door.
Dont do things backwards .....FIRST , I would make a decision what camper (floorplan) you need or like .
Add all your stuff and estimate a real rollin' down the highway weight. Most campers hardwall TC's are 3700-5500#, depending on the size and number of slideouts etc.
Now, go buy a truck to haul it. You might need a 550 , i don't know. Whatever set up you choose, make sure the COG of the camper is in front of the trucks rear axle for better handling and weight distribution.
If you buy a truck first, you are limiting yourself to find a camper to fit it and you might not be happy.
Bob