The Gen-1 body style went from 2008 - 2015 in the US, so those years should work for you. 2014 and 2015 were "facelift" years which look pretty much identical but changed relatively minor aesthetics including lights, grille, some interior pieces, etc. but it's still the same body style. The Gen-2 started in 2016 (2017 model for US).
There's been quite a bit written about what to look for when buying, but a solid PPI will be necessary. Common failures include magnetic ride, A/C compressor, oil return pipe (leak), and a few others you'll find repeatedly on the forum, but each is easily inspected during a PPI - granted, working one day doesn't mean it won't fail the next! So, just plan and budget accordingly. If you're looking at a 2010 or earlier car, the frame crack is indeed a "real thing." It's not something that's super common, but it's happened ENOUGH that you certainly need to inspect those cars. While Audi has continued to be helpful in resolving those situations (when they've occurred), it doesn't mean that will always be the case. So, if it was me personally, I'd just have a plan on how to mitigate the risk if purchasing one of those model years (e.g., proactively welding the reinforcement plates).
Drive multiple examples - including the "big" decisions on V8 or V10, manual vs. R vs. S, coupe vs. spyder. Also, have an idea of what options you're after. Some of these options can make/break the feel of the car IMHO - full leather, B&O, carbon trim pieces, etc. A well optioned car will feel much more luxurious than a bare one.
What modifications are you willing to accept (or looking for), versus what do you expect to be stock? Wheels and exhaust are two very common modifications, clearly - and while wheels are much simpler (and less expensive to swap out), an exhaust that drones, is too loud, etc., will be a bigger undertaking and expense. Are factory parts available to revert on other mods if you chose to do so?
Beyond the mechanicals, style, and options, there's obviously aesthetic condition to consider, too. Check the obvious things like paint chips and bolster wear. Some amount of both are expected on most cars, but a great example would be one covered with PPF (no chips) and with a careful driver who didn't rub the bolster on entry/exit. Those cars exist.
Get maintenance records PRIOR to a PPI - helps you identify things to take a second look at, and it'll help filter out cars not worth considering. Do NOT expect to get maintenance records after you've completed a sale. Audi will not provide a prior owner's records to you (or at least they're not supposed to for privacy reasons - many people have learned this the hard way). A well maintained car should have all of its services done annually and by the book. It doesn't need to be done at an Audi dealer, but there should be records of someone following the recommended process. A 10 year old car, for example, that never had the transmission fluid flushed, brake fluid changed, spark plugs done, etc., because the owner just barely did oil changes, is one to avoid.
Look for signs of abuse or neglect. Cars (coupes) left to sit outside may have rust and/or discoloration on the metal mesh that covers the sides of the engine bay - this is due to water constantly entering the engine vents and dripping down onto the mesh parts. Are the tools all accounted for in the frunk? Are the tires in good shape or bald? Are any of the interior trim pieces nicked or cracked? Some of these, like the canopy surround, are a huge job to change - requires the whole dash to come off. Is the leather clean (matte - not shiny / oily)? While very common, the shift knob can also attract lots of scratches from people who wear rings. Is the car generally clean?
Consider where the car has lived and what your intentions may be for it long-term. A car that's lived in a warm, dry climate, for instance, may minimize the chance that the prior owner(s) drove it through salt-covered snowy roads. While these cars are aluminum, corrosion can still occur, and there are plenty of susceptible parts - radiators, fluid lines, fittings, etc. - that won't take well to salt exposure over the years. That said, a car that's left to bake in southern sun/heat, can also have issues with leather, such as bubbling, pulling, or separation on the dash or door panels. Just things to check for as best as possible.
Good luck in your hunt!