One of the best, and safest, ways to explore the limits of the car and your own skill set is to take part in a NASA HPDE event like JHM2K mentioned. You're on a closed road course with an experienced racer/instructor to start out with. He'll talk to you about proper lines through the corners, proper braking points, etc. You'll be on a course with others who are just getting started, or of similar experience as you progress up through the ranks. Passing zones are specifically designated and strictly enforced, and driver's meetings are mandatory pre event and after every session.

I've done a few of these on different tracks and they are a blast. Threshold braking, max load cornering, WOT acceleration and everything inbetween, over and over again. It's a hell of a rush!