A street legal race tyre is produced with very soft R RACE ompound rubber.
Usually the original tread depth is around one eigth of an inch,quite often with very little tread pattern and of very little use if rain is on the track. I have found that the lowest aspect ratio,E.G. 40 will steer best. the lower the aspect ratio is , the more competitive the tyre should be, the higher the aspect ratio the more delay in resposes from the wheel.
Most of these tyres have a D.O.T. stamp on them , and are classed as D.O.T. Race tyres, Yoko , Pirelli,Hoosier, Kumho, Toyo and many more sell these DOT Race Compound Tyres. As far as I know slicks are illegal on the street,I have yet to try a set. My last set of DOT race tyres lasted only about 50 miles, but they were hard miles,round the slalom track pushing a 4000+ lb XJS and myself in the drivers seat. It has been a lot of fun the last ten years , learning things the hard way, learning to take it to the limit of adhesionm, sometimes a little beyond. More people are now interested in making their bigger Jaguars go beyond what they were intended to do. Being able to be quicker than any off the shelf Jaguar is quite an accomplishment,and quite a crowd pleaser.
As for different size rims ,I guess it all depends on the tyres mounted on them , sidewall height etc.
Any further questions re the Slalom Program Just Ask Art.