It was suggested to me several years ago to look into Hoosier A7 or R7. Since then, I have been looking at other brands such as Toyo Proxes RR and BFGoodrich g-Force R1. These are a DOT legal tires and are designed for autocross and competition racing. They are slick type tires and do come in a 13" wheel size. I have not yet gotten my car together, so haven't tried any of them yet. I do have a friend that uses the Toyo Proxes R888 series tires for road racing. The price doesn't seem to bad compared to some of the others.
Steve