OK, I have a Golf R on 19" Pretoria wheels (but am interested in an S3 in the future), pretty much the same car under the skin, and it came on truly awful Bridgestone Potenza RE050As. 6k miles in I changed tyres because the grip was truly awful, and went for Michelin Pilot Supersports (PSS) and the car is transformed - completely unflappable in the wet and the dry, even when pushing it very hard.
There are other tyres that are good to start with (Conti 5s, Dunlop SP01 etc), but they tend to rally fade hallfway through their life, Michelins are good down to the last 2mm, either PSS or PS3 (PS4 may be out now).