S3 standard wheels are 18 inches by 7.5J in width and the offset is ET54.
Ideal fitment to improve the looks but maintain usability would be 18 inches by 8J in width and ET45.
There are lots of good quality wheel manufacturers, many of whom make the wheels for Audi. Ronal, BBS, Speedline, Team Dynamics just to name a few. A popular choice that doesn't break the bank is Team Dynamics Pro Race 1.2. They come in the 'ideal' fitment I mentioned above.
Tyres wise keep the factory size - 225/40R18 92Y XL...popular choices seem to be Vredstein Sessanta or Vredstein Vorti as well as the Continental Sport Contact series and Michelin too. Goodyear Eagle F1 asymmetric 2 are very popular too.