I bought the wife a 2006 Envoy off Copart. It needed both driver's side doors, but only had 105k on it. I bought the doors at a local junkyard in the correct color and swapped them out. It still has a dent just beind the new rear door, but we don't much care... Total, I've got about $2200 in it, and she's been driving it for a year now. The I-6 is a smooth engine, and gets around 17-18mpg for us.
Issues: I don't know that anything is "common" for all years... Oh, yes I do. The center console is almost always broken loose. It doesn't like when people shift their weight in the seat by using an arm on the console...
After being mostly trouble free for the first 10k or so that we had it, ours is having a few issues with the cold weather... I imagine most of them may be due to the year it sat on the copart lot waiting to be processed... I just replaced the AIR solenoid, which was not sealing after being commanded closed. This caused a MIL for lean condition on a cold start when the pump ran. $120. I have a thermostat for it too, as the current one is sticking open a bit, resulting in below desired operating temps. $40. Finally the fan clutch seems to stay engaged once commanded. It's "thermo-electric", so a new fan clutch may be necessary, but I'm doing the thermostat first to see if that fixes the fan. $140 if it doesn't.. I also replaced the outer tie rod ends when we bought it, as one was a tiny bit loose. ($40)
Plusses: ALL GMT360/370 platform vehicles have a 2" rear hitch built into the frame. They were carried down the assembly line with it, and it's pretty solid.
The I-6 is a great engine IMO. It offers excellent torque, and was one of the first uses of Variable Valve Timing. ONLY the Trailblazer version will accept factory front tow hooks. They won't fit an Envoy. There is not really a good option for really HD front tow points aside from a low hanging front hitch. The Trailblazer hooks are NOT for severe use...
The 2006+ versions have stability and traction control, as well as some updates to the I-6. Traction/Stability is a plus for me, as the RWD platform is fairly tail happy in the slick, and it'll save my wife if she forgets to put it in 4wd. IMO, even auto 4wd can be a bit loose at speed, as it allows the rear to slip before engaging the front, and that causes the rear to step out a bit at times. In low range, the brake traction control works well to keep the truck moving even with wheels off the ground, but you have to stay in the throttle a bit for it to build brake pressure on spinning tires. Offroad in 4wd high range, you'll want to kill both traction control and stability control (Press and hold the button) so it doesn't shut you down if things get suddenly soft or sloppy. I'd recommend finding a truck with G80 option, which is the locking rear diff. It works excellent in high range. I'd also recommend 3.73 or 4.10 gears with the I-6. Yes, 4.10's were available, but not common... Many of them had 3:42 gears, which i would avoid in general if you plan to upsize tires anyway.
Lift: IMO, you will NOT get 35's on one of these without really significant trimming/bashing of the body, or a massive body lift. Max lift that I'd recommend in the front is 2". Yes, people do 3", but that's pretty hard on stuff... The problem is that the front diff mounts to the engine oil pan, which means you can't drop it at all. The upper control arm balljoints also max out at about 1" more droop than the factory allowed. You can flip them for a bit more droop, but then you have to watch compression travel too. I'd think a 255/75R17 on a stock rim would be about the max tire that will fit if you want it to remain a nice driver. Much larger than stock sizes will really sensitize the stability control on later model trucks. Kind of a plus, the undercarriage is fairly flat, with nothing really hanging down as a one way check valve for trail progress... Of course the down side is that it's all fairly low compared to a 4-runner or XJ Cherokee. For our Envoy, I cut 1/2" plate strut spacers for the front and that leveled it nicely with no ill effects. (~3/4" of lift) Nothing seems to bind a full droop, and if I wanted more lift, I could probably get it with a bit of preload in the struts. The rear is easy to lift with a coil spacer, but when you can't lift the front a lot, ease of lifting the rear is moot...
My biggest disappointment: The hood has a prop rod. For some reason, it just seems to me like it should have springs or a strut. This gets me every time I open it...