Herimpression - you are getting a lot of information from a lot of individuals. The information is good.
I went through the remorse part and the first camper was a 19ft 7000# Pilgrim towed with a 2004 1500 Silverado Ext Cab 5.3L. Traded it for 30ft 7820# Innsbruck bunk house with 1 slide. The 1500 was having trouble with 230 deg transmission temps. Bad idea. Upgraded to the 2005 Silverado 2500 4x4 Crew cab with 8.1L. This will tow 12000# off "bumper" with a weight distributing hitch or 14000# 5th wheel.
Trailer Life has towing guides that are very accurate. This is where I verified the towing capacity of my vehicles.
When I went looking for the new trailer, I knew what GVWR I wanted to stay under. All trailers have that number on a sticker (usually on the right side as you look front to back or in a cabinet).
Visit the TT manufacturer web site and find several before going to the dealer. If the web site only shows dry weight and carry weight, add them to get GVWR. Many of them have a bunk house trailer with slides for less than 7500#. I know, I've looked.
My truck does not even act like there is a trailer back there when towing. I just can't pass a gas station.
I just know a 1500/F150 (half ton) usually will not be good towing anything over 7000#
If you are going to get a new (or new to you) truck, I would like to recommend the following as I just finished looking for a new truck when I got the 2005 8.1L 2500HD Crew Cab 4x4.
1) Chevy 2009 or newer 2500HD 6.0L with 4.10 axle ratio.
2) Chevy 2004 or 2005 2500HD 8.1L with the Allison Transmission
3) Ford 2012 or newer F250 with the 6.2L gas motor.
4) Dodge 2013 or newer 2500 but check Trailer Life.
Each one should pull 9900# or more with a weight distributing hitch
Good luck in your search. This is just my two cents. Each one of us giving you information has their preferences.