The Michelin's Pilot Sport PS 2 would be my choice, and from what I've read so far they seem to be among the best for what you want.
Does the car go to track often (or at all)? If so, an R rated tyre like the Pirelli P Zero Corsa System (like the ones in the Stradale) or the Toyo RA 1 wouldn't be a bad choice. They wouldn't last much, but they grip like hell...
But if you don't go to the track, it's better to stick with a regular street tyre.
Any one of these will be a good step in performance, compared to the Continentals:
- Pilot Sport PS 2;
- Potenza S-03;
- Potenza RE 050;
- Pirelli P Zero Rosso;