Do a search on this subject a read for a weekend!!
There have been a lot of advancements on the ability of trailers to be towed with a shortbed. . A lot of trailers have clipped front corners and a little longer pinbox so you can do almost a 90 deg turn. . .
I thought I had this down pat when I had a 2500 and a big 5th. had a thing called a RV5. it was a 10" extension of the kingpin and it worked pretty good til I put a $500 hole in the front corner of the trailer. . so I got the 5th airborne Sidewinder. . see a few posts near this thread on this. This is a dream. no sliding 5th wheel hitches or whatever, just a better pivot for shortbeds. . it also has an airbag on the hitch to help the ride.
Now, as for weight...
I towed a 36' 5th wheel which was too heavy for it but I compensated for it with good power, brakes, jacobs E-Brake, and "F" rated 19. 5" 12 ply tires... What is recommended is around 10-12K load max. . mine is 15,500#. with around a 3000# pin... I also had a suspension add-on that helped the on-board weight ability. .
If you have stock engine, brakes, and "E" tires, best to get an E-brake a least and some gauges. for Fuel Pressure, boost and pyro. If you have the overloads on the 2500 which is the towing package for it, then the 10-12K trailer is good for it. . It could take a little more. . like 13K at the outside.
The salesman will tell you that you can pull a big 15 or 18K with that just because it is able to be pulled by a shorbed with the clipped corners. . they have no clue on weight ratings or ability.
So when you look for a truck, no big lifts with big tires. . not good for 5th wheel pulling. . A tow package and light package will be good as it will have the bigger alternator. Any moderate power add-on is good as it won't get the engine too hot when towing.
On the older trucks, the 5600 manual is good for pulling especially if you have a South bend clutch or equivalent. Don't have any clue to the Autos but a lot of people have done ATS upgrades to these to make them able to tow a good weight trailer. as well as deeper trans. pans and such.
Hope this info points you in the right direction for upgrades. good luck