Shouldn't I at least get a set of track tires?
No! In fact, we actively discourage students from using performance-enhancing modifications, especially track tires, at our schools. To understand why we do this, you have to understand that modifications that increase your speed also decrease your available reaction time and thereby may compromise your safety.
Track tires (e.g., BF Goodrich G-Forces, Yokohama A032Rs, Toyo Proxes RA1s) are both a blessing and a curse. They will inhibit your learning by removing the requirement for driver skill to improve your speeds. In addition, the higher speeds they allow mean a corresponding decrease in the time available for you to react to an impending loss-of-control situation. To maintain your safety, your speeds must increase commensurately with your developing skills. Performance-enhancing modifications provide an immediate jump in speed with no corresponding increase in skill. This is not only counterproductive but dangerous as well.
Track tires do have the advantage of wearing better when stressed, and they do provide more direct feedback (a crisper "feel") from the road. However you will learn far more by having to overcome the limitations of regular street tires, and you will be a much better driver as a result.
The appropriate time to switch to track tires is when you have exhausted the performance available with street tires, and your car-control skills, as evidenced by your skidpad performance, are sufficient to address the sharply reduced reaction time afforded by track tires.
We encourage you to discuss consideration of track tires and other performance-enhancing options with your instructor before obtaining them.