My friend is a Volkswagen dealer GM, so I'm pretty familiar with the Atlas. So, first comments about that, and then comments about new models in general.
The Atlas is on the MQB platform, so the same platform that the Mk. 7 Golf, A3, TT, and the incoming Gen. 2 Tiguan and Gen. 7 Jetta (Tiguan is out now in Europe and is coming in August to North America), Gen. 7 Jetta is next spring/summer. This platform has been really reliable, the Mk. 7 Golf's and A3 don't have any major problems that stand out, and they're doing really well in long-term reports. Of course, the Atlas is by far the biggest vehicle on the platform, but the fact MQB has been so reliable should be reassuring. I haven't heard of any problems with the Atlas in the two months it's been out either. It'll be under warranty for four years so I'm not sure why you're thinking about aftermarket parts already. 4Motion (Haldex based AWD) is pretty reliable, and the engine options are venerable. I've got a Touareg TDI and was thinking about an Atlas (also got two kids, a 2 and a 5 yr old) if they end up offering buybacks on the 3.0T diesels, but I'm not a huge fan of the lower end trims on the Atlas. I'd have to go into the 60K after tax range to get a similarily equipped Atlas, and at that point I don't really see much of a use not just getting a Q7 (which is also a 7 seater).
For new models in general, it really depends, mostly on the make, and whether it's a new platform or not. As an example from VW, the 1st Gen Touraeg/Q7/Cayenne was really bad for the first few years because it was a brand new platform with a whole host of new tech. First models (regardless of newness of platform) from the Japanese brands tend to not have major kinks, while first models from European tend to be pretty buggy if they're new platforms. American cars are can have bugs just about anytime.
You've got a warranty, and honestly as long as you take care of your car (regular maintenance and check ups, not just oil changes from your neighbourhood quick lube), there is nothing wrong with new cars. Reliability reports in general are a bunch of garbage, and can be explained by 1) driver habits 2) driver stupidity.