Since you specifically mention "truck " in the title of the thread...It's hard to beat a GMC Sierra for a smooth-riding truck, stock, right out of the box. The Suburban, if it is not too long for you, could also be a a real comfy ride. They are , essentially the same thing.
The brand new Ram trucks ride very well. But your budget of 5k to 7k rules them out.
I happen to have a GMC Sierra and find it rides like a Cadillac. Having said that, if I were to get a chance to pick up a third vehicle, I'll probably grab up a 2013 Tahoe Z71. That would also do very nicely.
Getting a lift and bigger tires wont necessarily get you a more comfy ride unless you need that extra height to get up over debris or obstacles. For me, I remove the "chin strap" that GM places along the bottom edge of the front bumper. That's a big help in terms of clearance, since it's really only there as a wind spoiler. If after that you still want some lift and want a comfy ride, you might just consider leveling the front end, which comes stock with a bit of a downward rake. l have heard great things about Bilstein 5100's. I plan to use the Bilsteins in my Sierra when I change the old shocks out soon. I've heard they are the best ride and they are adjustable, so you can level up the front end.
...Someone mentioned cranking the Torsion bars...that will get you lift, but it will actually harshen the ride quality. Anyway, the newer GM k1500 products dont even have torsion bars anymore, they have been coil-overs since 2007. Coil overs provide superior ride comfort in conjunction with thier Independent Front Suspensions.
I wouldnt even go overboard with the tires, if you plan on being on forest roads. You probably wont need something like a Duratrac or a BF Goodrich All Terrain. They are great tires by all accounts, but for forest roads, you probably wont need something that aggressive. Based on what you've written, you'll be on packed dirt or gravel, not so much rock crawling, I'm guessing. Goodyear Trailrunner, BF Goodrich Long Trail, Rugged Trail, or Falken Wildpeak should do you very well.
If fuel economy is at issue, I can tell you that my 2014 Sierra 5.3 liter V8 gets the same fuel economy as my 1999 Grand Cherokee 6 cylinder 4.0 liter. Mainly because of the newer GM engines making use of cylinder deactivation/ Active Fuel Management. The brand new Colorados and Tacomas dont necessarily get any better fuel economy, either. So smaller isnt always better, and often does not have the ride quality.
So, in a nutshell, in my eyes, for what you are asking, find a 2007 or newer stock GM (Chevy or GMC) full size K1500 truck (Silverado or Sierra) or full size SUV (Tahoe, Suburban, Yukon, Yukon XL) with the Z71 package, front bumper chin strap removed, and Bilstien 5100 shocks up front and even only moderate offroad tires will get you exactly where you want to go in comfort and ease with plenty of room for the significant other, the dog, and all the gear you could need to carry.
