I'll start by saying if reliability and ease of repair are the priorities, then you should be looking at Toyota/Lexus, Honda/Acura, etc. ATS's are not expensive to buy but [any] luxury performance car is not typically inexpensive to maintain. Like buying an e38 7-series for $3500 and then having to shell out $4k for the OEM replacement suspension, I'll never forget the kid on my Accord forum that went through that. That's an extreme example, but it's the same principle. So just know what you are getting into with an upper tier car. If you can wrench on the car yourself that will save you some money. Also don't forget an AWD car is more expensive to maintain than a FWD or RWD car.
That said, here's the deal with the ATS. Quality control was inconsistent so if you get a bad car you'll have all kinds of ridiculous issues but if you get a good one it seems to be a pretty solid car. So I usually recommend that people get a certified pre-owned example so they can find out what type of experience they are going to have while still under the protection of a warranty. I believe the timing chain stretch is a thing with pre-ATS 3.6 motors but I'll let more knowledgeable V6 owners speak to that. I have seen a handful of 3.6 motors go out, but it's generally more common to see issues with the 2.0T. GM gave early 2.0T's a lean tune and the wrong spark plugs, which did result in some blown motors. But it's all relative, you have to keep in mind there were more 2.0T's made, and most people don't go on the internet to talk about how great their car is doing. Personally, I believe if you use 93 octane fuel, use low ash full synthetic 5W-30, Don't lug the motor, follow good FI driving methods like not getting into boost until the car is at operating temperature, perhaps run catch cans, etc. the 2.0T will be fine. 2.0's from Audi, Subaru, and other carmakers have had the same issue, and the problem is the average consumer isn't in tune with what a turbo motor needs to last. So many instances of 2.0 issues could be owners not using 93 octane fuel, or the wrong oil, etc.
So what are the undeniable things these cars are known for in terms of issues? Rear axle seals leaking, CUE screen delaminating, Cam solenoids failing, and the autos have torque converter issues. Though it seems more common with the 8spd auto, and I believe reflashing the trans tune and changing the fluid is supposed to have fixed that (there was/is actually a lawsuit against GM for it). There was an issue with the steering rack bolts but that's free to fix under the recall. That's kind of it for major stuff. But the CUE screen issue is so widely known now that there are many aftermarket solutions out there so with under $200 and an hour or two of your time you can replace your CUE screen yourself. The cam solenoids are not expensive to buy and they are very easy to get to and replace, so neither of those are that bad. The 2.0T timing cover is known to display "seepage", but it is not really an issue it seems as almost any one you look at has it and dealers usually don't reseal it unless it's visibly dripping.
My ATS is a 2014 2.0T 6spd manual Performance trim, I bought it CPO at 26k miles, it has 46k miles and it has been a great car. I did have to get the axle seals replaced once. Other than that it's been just oil changes and tire rotations. I was able to get the timing cover resealed which I was thrilled about haha, but it was not causing an issue prior. My powertrain warranty ends this May, but I plan to keep the car because I love it and there's nothing else I really want that offers everything the ATS does at this price point. The cars are plentiful enough that parts are not hard to find nor afford. Finding a RWD sport sedan with a manual transmission is really challenging these days too. I also have to say I love that the ATS is on the rarer side than say, a 3 Series or C-class, for better or worse. I like driving a car you don't see constantly everywhere.
Perhaps you know this, but GM benchmarked the E46 3-Series for the chassis and handling dynamics of the ATS. The ATS is widely known and praised for its handling, near 50/50 weight distribution, good steering, and light weight. And it's cramped back seat haha.
Also the aftermarket for the 2.0 is pretty healthy, if you plan to modify the car at all.