When you start talking "larger camper" you really need an 8' bed. If for no other reason then you'll have about 10 times more options when looking at used campers. I think you'll really be sorry if you go with a short bed truck.
I agree, 2 or 3 people don't need 4 doors but unfortunately most extended cab trucks now have the "suicide" rear doors. I hate those. Trying to put anything in the back seat while parked between other vehicles is practically impossible. You have an open door on each side of you and not much way around. I used to have an ext. cab truck with only 2 doors and the front seats slid forward. It worked well. The ext. cab truck I drive at work has the rear doors and the seat doesn't slide. My personal truck is a crew cab and it works great. I much prefer that arrangement. Also, resale of a crew cab is usually much better than anything else.
You won't necessarily need a DRW unless you get one of the largest campers. I would strongly recommend you get a 3500 series or "one ton" truck over a 2500 series. Depending on the make and model you may gain stronger rear axle, rear springs, wheels, tires, overload springs, etc. All of these are quite desirable for hauling a TC.
Which truck? If you like your Chevy I'd stick with that. I've had great service out of every Chevy I've owned. For your particular situation I would look for an 8.1L big block with the Allison automatic. This would have a great engine, great transmission, and plenty of power. It will only get around 10 MPG and they only made them from '01 to '07 so they are increasingly hard to find.
I had a 1996 Dodge. It was a great truck except for the automatic transmission. Dodges from the 90's had terrible transmissions. Up until they started the 68RFE somewhere around 2005 I think they had by far the worst automatic. I think the Allison in the GM trucks is the best auto you can find in a "newer" truck like you're looking for.
I just flat out don' like Fords. My Dad had one that was terrible. We were happy when it got stolen. My work truck is a '03 F-350 and compared to my Chevys it starts hard, idles ruff, handles bad, the seat is hard, it has no traction, etc. It's the most time I've ever spent in a Ford truck since I've been driving it and if there all like that I can't imagine why anyone would buy one.
Happy camping and good luck looking for an 8.1 big block.