Hi there, first up welcome to the forum.... Protracted ramblings follow!
As a reply to your post, I own a A3 TDi q and I can only talk about my experience with it and dont proport to being an expert though there is a lot of experience and knowledge on the forum.
Your right about being difficult to find, be prepared to travel. Audi Used/Abused/Approved may be a good starting point though they do crop up elsewhere with independents. There may be some general info on buying which is common, have a look at the sticky threads up top here. Remember, its a car and all the usual car buying checks work on Audi's. Less danger of being a Chav Chariot though there have been some shocking photo's inthe threads.
I have owned mine as a 52 plate for 75k miles now. Bought with 5k on the clock. Superchipped at 5k. Its run without any problems whatsoever. Nothing fallen off, creaking, failed or not working. Never failed to start and copes with Scottish weather brilliantly (god bless seat heating). It uses little or no oil between services which are approx 18k apart. It gets serviced by Star Performance, an independent garage, and they do a great job. No actually, they do better than that. Think of your Audi dealer as a sales outlet formost, then service it elsewhere.
It has had several trips to the continent, Germany, Italy, France, etc etc and has coped well with running at speed for hours loaded to the roof. Expect 40ish mpg on average, up to 44mpg if carefull and 36mpg if your having a good time on the twisties. Go for it on the Autobahn and see little better than a petrol model. Approx 600 miles per tank of taxes is not too difficult.
Elsewhere folk seem to agree that the engines are good for mega miles and robust. Mine didnt loosen up properly until circa 25k miles then the mpg improved quite a bit. The interiors are sound and well put together. Assuming your after a Sport model, it will be 130 bhp, easily raised to 180 or so... has climate control, white dials, sports seats, and other options..in dash 6 disc cd and other stuff. It was a run out model so may have a good equipment level to empty parts bins at Audi.
Running gear seems to be a curious mix of A3 1.8T Q and Audi TT. The Haldex system again seems proven and reliable as long as oil changes and routine maintenence are followed, same for most cars. It doesnt share much with the S3 model in brakes or suspension. Finding these items may be a bit frustrating as its a scarce model and not often listed in its own right. It seems pretty tough too. I hit a concrete sleeper that had fallen off a lorry on the motorway. At 80mph in the fast lane.... The front passenger tyre blew and both passenger side rims were bent, but it stayed in a straight line and got me on the hard shoulder under control. When Audi checked the car over there was no problem... Over engineered but its always a good feeling of solidity.
Overall, I love it as a good mix of sporty and sensible. An S3 it isnt, a fast diesel it is. If you hav'nt driven a haldex type 4wd it needs a change in driving style to make it work properly. Mine is a keeper, and after reading some of the problems with the newer A3 2.0 TDi / Q in a way, though I dont have the latest, I do have something that is the last of a very well proven an developed technology and I hope it will be around for a while.
Hope this helps and you find a good one!
Have a search around, there are a few folk with the same car, The Slug, for one..... There is plenty of info, just needs hunting out!
