The basic combo would be chip cam intake and exhaust. These should cost under 500.00 but wont yield mid 14s. You will probably see 135-140hp. Nitrous Forced induction or extensive engine work/swap are the only ways to get to mid 14s. Nitrous is you best bang for the buck.

Why dont you buy an older Rabbit and swap in a 16v engine? With out any mods the car will have a better hp/weight ratio than the A3. With head work euro cam exhaust and close ratio tranny the car should run low 14s if not better.

Good luck!