I have a 2006 4WD with the crew cab and 5.7.
It has about 96,000 miles on it.
I bought it used with about 30,000 miles on it specifically for towing. I work from home as a consultant, and we mostly use our 2004 Toyota RAV 4 for "commuting" duties. But it has only about 104,000 miles on it as well.
Mine has 20" wheels and tires, so it's tow rating is only about 7700 pounds. That's just enough for the trailer you're considering.
It's expensive to maintain correctly. For example, it costs $300 to change the lube in both diffs - EVERY 30,000 MILES!!. Oil and filter are normal, but it takes a bit more oil than a car.
I've also done a complete transmission flush, coolant flush, brake fluid flush and so on. All of them pricey compared to a "car."
Stock shocks suck,
so I put on Bilsteins. They are amazing. But turns out the fronts are "struts," so I needed a shop to do the job, and the lower mounting bolts were frozen so that cost $600 in labor.
Factory brakes suck,
so I replaced the fronts with these...which are awesome. This was an easy DIY project in my driveway.
Meanwhile, I have the factory plugs, fuel injectors, exhaust system, CV joints and boots, U-Joints, and so on. Starts instantly, and purrs like a kitten.
Mine was a Laramie model - automatic 4WD plus manual 4WD and low range all on a dash knob. Leather, dual climate control, heated seats, Infinity stereo, power driver's seat, power pedals, and some VERY desirable fold down floor boards that hide under the rear seat. When the rear seat is raised, this make a flat load floor...a must have.
The good news is that a used Laramie is likely to depreciate to very close to the level of a "lesser" model. My wife loves this truck so much that anytime we go anywhere together, we take the truck. Big, smooth, quiet, and with the Bilsteins, very secure handling for a truck (it wallowed from day one with the factory shocks).
Depending on where you tow, this truck is "adequate" or better, My rig is 4000# wet and ready, and I carry nearly a half ton in the bed. I live in the Rockies at 8300', so the thin air saps the power a bit. In the mountains, I keep it in OD off, and I spend a lot of time in 2nd gear. 2nd effortlessly maintains 60 to 65 mph (I have a tachometer). The transmission appears to be a 3 speed with electric OD...not a true 4 speed. Down the hill, around Denver at 5280' and on level ground, it cruises along in tow/haul mode with little effort when towing.
I shift manually all the time. Descending a 11,500' mountain pass, you'd better gear down. You won't see my brake lights very often even going down
Red Mountain Pass. Once again, 2nd is ideal, and no strain for the truck. What I don't do when climbing is force lots of up- and down-shifts, lots of gear hunting, in the mountains. It's far easier on the transmission to select a lower gear an hold it, and not have the damned thing upshift when you lift off for a curve, only to have to downshift under load once you hit the straight. This matters little at sea level on the flat, but even in the Blue Ridge Mountains, this tactic will baby your transmission. Meanwhile the 5.7 spins happily all day 1000 RPM below redline.
You can expect any older "half-ton" to work harder with about 7000# wet and ready on the hitch. But the truck is up to the task.
Consumer Reports says RAMs are worse than average or much worse than average on reliability. I haven't experienced that, but, as you've read, I take care of it, and bucking the odds doesn't make it so across the board. The good news is that they are common, and pretty much any decent private auto repair shop can handle them.
I'm sure you've heard this many times. Budget about $200 for 2 hours of mechanic time and have someone you trust go over a prospect thoroughly (not just a quick once over) before you invest. If you buy a bad one or one that's worn out, it will eat you alive.
It sounds as if you don't plan to commute in it. Good idea! Downhill with a tailwind I get 17 MPG. Normally, when using it as a date nite vehicle, I get 15 MPG. Towing, I get 7 to 10. My 20's cost $1000 to get reshod. And all the routine repairs cost almost double what they cost on the RAV 4. Leave it parked when you can.
By the way, the Firestone air bags are worth the investment. I don't need a WDH with my big PUP, but even with a WDH, the truck is sprung softly. The airbags prevent porpoising, ass sag and headlights pointing skyward, and so on.
Also make absolutely sure that your favorite example comes with a full tow package. If it has an after-market hitch, walk away, because it will, very likely NOT have the transmission cooler, larger radiator, larger alternator, factory installed 7 pin harness, and so on that comes with the tow package. Even if it was added later, the factory package is better integrated and more reliable. There's nothing quite like a cobb-job wiring harness to drive you crazy. It might not even have the tow/haul mode on the transmission. If you stumble on a "stripper/work" version of one of these trucks, pay close attention to whether it's setup for towing. Also be sure it has the original owner's manual...not only for the info, but also to ensure that the tow rating on your truck matches the claimed tow rating in the manual. A replacement owner's manual from a salvage yard could be way off on a lot of things, from tire pressures to maintenance intervals and fluids. A replacement or lost owner's manual is a sure sign that the previous owner didn't give a rat's ass about the truck.
There's no free lunch to tow a 3 1/2 ton trailer. Don't even think about it with a unibody SUV. Tahoes and their kin are no more reliable than the RAM, and apples-to-apples, you'll likely pay a bunch more for a Tahoe or Suburban. Jeeps and Durangos are sisters to the RAM, but a whole lot less in many ways when it comes to towing. A big trailer and a relatively short-coupled tow vehicle is asking for trouble when a semi tries to blow you off the road. Ford and Chevy half-tons are only a smidgen better on reliability. You won't touch a Tundra for your budget, and as trucks go, while they are Toyota reliable, they are vastly inferior trucks and handle far worse. And don't go near a Nissan Titan with a 10' pole. They had REAL reliability problems according to Consumer Reports. Is a RAM the best choice? Perhaps not, but in the real world realm of just 3 choices, they are more or less equal until you get to Ford's aluminum bodied, turbo engined models, and they are clearly superior.
Stay away from anything that's lifted or otherwise altered for off-road use. These things aren't much good after being beaten to death in the boonies. And the last thing you want to do is spend $1800 for a set of tires that wear off in 15,000 miles.
So, that's my real world experience with the very truck you want to buy. I'd buy another in a heartbeat, but I'd be damned careful which one I chose.
My 2 cents. Worth every penny you paid for it. The photos show the truck and an example of where it takes us. That spot is about 5 miles into a primitive dirt road into the Pike National Forest on top of a ridge in "South Park" (yes, THAT South Park). Boondocking at its best. That was March, 2017.