I'm a GM guy so I can't help with the Ford equivalents. Since you live in NC with it's foothills I'd want a 3/4 ton. In the GM the 6.0 gas engine with 6 speed auto and 3.73 gears would fill the bill. My 6.0 has 4.10's and handles 13,500 easily.
I don't know about smaller engine as I was always a big block guy until I got down sized by the government. Since it looks like you'll be traveling with more than just the DW I'd go for the 8' bed and bigger gas tank. Of course tow package, posi-trac, 4x4 and love the extendable/foldaway electric mirrors. From there you can just keep adding whatever you like, (make sure to ask the DW also).