Late to the game, but I can't agree enough, 01-06 is the right answer. I have had an 01 suburban from 240k to 360k, an 04 yukon XL Denali from 170k to 255k and counting, and a 2013 Denali XL from 180-240k and counting, but slowly, because the engine is shot due to cam issues starting with the DOD failure a month after we bought it... I want my wife to ditch the 13 and drive the 04, but she likes the creature comforts in the 13, so I'm going along with it. All of them have needed a transmission, both Denalis right around 200-220k, the 5.3 at 300k (but it had regular synthetic fluid changes its entire life). I like the 4 speed better than the 6, but that might just be me. The 6.2 in the '13 runs strong, but I've had more issues on that truck than the other two combined. Interior is better in the 01 and 04 to me, wife likes the 13 better. But considering she picked me, I think it's safe to say her judgement is compromised...
I also have the 87 but it is not a DD, so I'll leave it out. If I include my parents, we had a 79 3/4T burb, a 93 suburban, a 2003 yukon, 04 tahoe, 09 tahoe, and 13 escalade. Again, the 03 and 04 had the least issues, 09 had the most, 13 has been good but it is also the lowest mileage and continues to be low miles, I think Mom does about 2500 miles per year...
If I was looking for another one, I'd go 03-06, plan for a transmission somewhere between 170-220k, earlier ones may have some ABS module issues, but those have probably been fixed already, all may have the gauge cluster issues that can be fixed for not much time or money, pull the bezel and send it to a repair shop. Otherwise? Brakes, tires, oil changes... Maybe a water pump at 150k? They are easy to work on, easy to reach, the only job that has been a pain was an AC clutch on the 2001 with 330k or so, it was a little awkward to get to. I have changed water pumps in half an hour, alternators in 10 minutes (mostly due to me being a cheapskate and swapping parts from one to another, along with my 5.3 swapped Monte Carlo). There is a rear heater tee that can be a pain, but it's the same tee on all of them from the 90's until at least 2013.
In my mind, these are the best compromise, taking nearly a century of GM experience to build a solid truck, adding computer aided design to the mechanics of it, but before the computers took over the entire truck and the EPA made them start using tin cans and aluminum foil to make them out of. Seats are comfy and cheap to re-cover if you have the typical wear on the driver bottom bolster, look good as a 4WD Z71, or as a Denali or Escalade, or just in the middle with a clean LT trim... Also, when my wife rear ended someone in my 04, totaling ours in the process, Dad and I were able to rebuild the entire front end bodywork in a weekend, including picking up most of the parts from local yards. I think I spent about $800? It's not perfect, but it wasn't perfect before, either.
Oh, the DOD theoretically saves gas, but my experience is that the cylinders on the SUV's only shut down under about 65 mph. On a 5 hour trip with ours, I think it only dropped to 4cly mode for about 2 minutes total, when going downhill. At 75, it stayed in V8 mode the entire time. Dad's Z71 pickup would drop into V4 mode up to about 70-72 or so, which does make an impact. Or did, until he went up one size on the tires and made the system useless again.