You will see a MASSIVE improvement from uprated pads and discs.
You're pretty close to me so I can demonstrate at some point if need be, but I am running 288mm fronts and 256mm non vented rears, so completely standard sizes but aftermarket discs and pads, and Nick from here who has uprated discs and pads on his S3 even commented how much better they are compared to his.
The right disc and pad choice makes a big difference.
Basically, the best discs I have had to date are black diamond grooved. They were approx £120 the pair of fronts.
These are also popular in the VW scene, its useful to take a lot of information from the Mk4 GTI owners as they are far more numerous and its essentially the same car as the FWD A3 T Sport.
Drilled discs are a no-no if you intend to run them hard, so its best to stick with grooved.
I use Ferrodo DS2500 pads on the front which are a dedicated track pad and have some of the best cold biting characteristics of any track pad. Obviosuly they work superbly when heated but the DS2500s are fantastic cold too.
The other pads I would consider would be Pagid Blue, Pagid Yellow and Ferrodo DS3000, depending on your usage.
The rear brake bias is about 30%, so you don't need to upgrade the rears really, so I run Brembo MAX on there and standard pads (Textar).
Its remains to be seen if standard pads will survive a track day, as previously I ran EBC greens.
Don't, whatever you do, consider EBC Red stuff pads. They are cack.
Not considering Brembo upgrades, my brakes are the best out of anyones A3/S3 and Mk4 GTI I have ever driven.
To give you an idea of price:
Black Diamond front Discs from Venom Motosport £120
Ferrodo DS2500 from Jabbasport £135
Brembo Max Rear discs from GSF £30
Audi rear pads from a Dealer £30
So total price would be £315, you could downgrade to Mintex fast road or similar pads if you dont intend to track it, which would save you £70, or upgrade the rears to Black Diamond grooved rears for an extra £70.