I'm in the same boat you are. I have a set of PSS on my car with less than 800 mls and have track days this month and next. I'm going to see how they do compared to my contisport3s which were not so great but do have plans and highly suggest to get a dedicated track tire/wheel set up. Hankook ventus v12, Kumho Ecsta sport, Direzza sport dz101 come highly recommended from Nasa GTS racers (for use before they started racing competitively). The apex rims are great, very light and also not incredibly expensive. You should be able to get a decent tire/wheel combo for a little over $2k.
Keep in mind no street tires, apart from DOT R compounds, are designed for track use, some just perform considerably better than others. Michelin Cup Sport as someone mentioned would be a step up from PSS but they are very expensive. My plan is to use one of the above mentioned tires for a half a dozen or so events before stepping up to DOT R comps Toyo R888 or RA1, Nitto n-01/5.