Which tow rig?

I recently purchased a 40' fifth wheel toy hauler, triple slide. The dry weight is 14,050 lbs., I figure 1000 lbs. of gear, my motorcycle is about 950 lbs., hers is 650 lbs. We try to two with minimal onboard water and empty grey and black tanks. I currently have a 1996 Ford F-350 DRW with a 7.3 liter Powerstroke and auto trans. It gets the trailer where it needs to go, but it really struggles on the hills and starting off, plus it is really old and I worry about the reliability. Fortunately our favorite camp grounds are not very far away, but we want o start venturing further. So my question is this, who runs a trailer this size and weight and travels long distances with it and what tow rig do you use and how well does it do. I am looking to buy a new truck, but not sure what to buy. Do I really need to look at medium duty trucks like an F-650 or a Kodiak? The guy I bought it from pulled it with a Chevy 2500 with an 8.1 gas engine and said it handled it just fine. Not sure I really would go that route, but maybe the motor is preferable but in a DRW. Any experienced advice is welcomed.