What should I check before buying a used Audi A3?

So I finally bit the bullet and decided to look for a used A3. Ive been driving my old beat-up Civic for like seven years and honestly it just doesnt cut it anymore on my commute into the city, so I figured it was time for an upgrade. I really want something reliable but still fun to drive, and my budget is sitting around 15k, maybe 17 if I find a perfect deal.

I went to check out this 2016 A3 yesterday, and man, it was such a headache. The guy swore it was dealer-serviced but the paperwork looked sketch as hell. I know my way around engines enough to spot a leaky valve cover gasket or a crusty coolant hose, but these modern Audis are just a whole other beast. The DSG transmission felt a bit jerky in low gears too, which made me super nervous. I mean, is that just a quirk of the dual-clutch system or is the mechatronics unit about to give out? I dont want to buy someone elses nightmare.

I really need this car to last me at least another four or five years without needing a total rebuild. Im in the Chicago area so the winters are gonna be brutal on the suspension and electronics. I feel like Ive read everything on the forums about the timing chain tensioners and water pump issues, but what else am I missing? Is there anything specific I should look at with the Quattro system if I go for the AWD model? I just feel frustrated because finding one that hasnt been abused by some kid who doesnt know how to warm up an engine is like finding a needle in a haystack. What am I missing here before I pull the trigger on one of these things...