First thing to do, is figure out what trailer weight, actually fits in your ratings.
Forget about that 10,000 lb (marketing number) tow rating. You will exceed one or more of your other ratings, before you get close to that trailer weight. Normally the first one is payload.
As the manufacturer, dealer, and consumer, add options, accessories, people, and cargo, the available payload and towing capacity are dropping, pound for pound.
On your drivers door post, there is a tire and loading sticker. It will show a max weight for occupants and cargo. That was the truck's capacity to carry, when it left the factory. Anything added by a dealer or consumer, would take capacity away from that. A fiberglass bed cap can take approximately 200 lbs.
Take that occupant / cargo number and subtract the weight of accessories, people, pets, and cargo you plan to take in the truck. Then subtract another 100 lbs for a weight distributing hitch. What you have left over, is the truck's remaining capacity to carry the tongue weight from a trailer. Divide that remaining capacity number by .13. The result will be a loaded trailer weight that will put your truck in the ball park with it's max ratings for payload, GVWR, and GCVWR.
Example:
Say your sticker says 1700 lbs for occupants / cargo and tow capacity is 10,000
Say your people / cargo weight is 800 lbs (including the WD hitch)
Remaining payload is 900 lbs
900/.13 = 6923 lbs loaded trailer weight
Average camping load (dishes, pots and pans, camp chairs, BBQ, bedding, groceries, water, etc) is 800 - 1000 lbs.
A trailer with under 6000 lbs dry weight, when loaded for camping, would put the truck near it's max capacity.
It's difficult for us to make recommendations, when we don't know what size / weight will fit your situation.