First, for the travel trailer weight you're looking at, you'd be fine in a lower trim (Big Horn or lower) half-ton with the 5.7 Hemi and at MINIMUM 3.55 gears, you'd be better served with 3.73 gears or ideally 3.92's. But that's going to severely limit what you can look for. You could make it work with a higher trim truck, but your tow capabilities and payload are (from what I've seen from some guys on here) drastically hurt by all the extra 'goodies' those higher level trucks get. So long as you properly set up the truck, trailer, and weight distribution system, that is. If you're not sure on how all that stuff gets set up, you might be better to look for a 3/4 ton gasser, as there are less maintenance costs involved. Be warned, 3/4 and 1-ton truck prices are EXTREMELY inflated right now.
Second, I would suggest you get your camper choices narrowed down to a couple different layouts that you like - they're generally all close to the same weight regardless of brand for similar layouts, and often the same layout can be found across 3-5 brands. I usually say buy the right truck for the job, so deciding at least close to what you're going to buy for a camper before you buy the truck is a good idea. I'd hate for you to buy a half ton truck then decide you want a 10k camper that will be more than the truck can handle.
Whatever you buy, look for something with a built-in trailer brake controller, and make sure it works before you buy (if it's a dealer they should be able to demonstrate, if it's private party see if they'll let a mechanic of your choice look it over). If the trailer brake controller is built-in you have a higher chance of the truck having actually been built with a tow package...but that isn't a sure-fire way to tell since people add them all the time. Only way to really tell is to see or look up the VIN and window sticker.
See if they can show you a maintenance history on the truck. Carfax, for all its faults, can at minimum bring to light serious repairs and/or if the vehicle was imported from Canada properly.