Can your current tires make it through your first track day?
I would recommend taking the car out for your first track day as is. Then after that get a feel for where improvements could be made based on your experience that day. Then start to consider how different sizes and different types of tires could impact the characteristics of the car on the course to accomplish those improvements and make a decision from there.
I would recommend taking the car out for your first track day as is. Then after that get a feel for where improvements could be made based on your experience that day. Then start to consider how different sizes and different types of tires could impact the characteristics of the car on the course to accomplish those improvements and make a decision from there.