Track wheel/tire sizes

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Trying to go from street tires and wheels to better track set up. My 991 C2S has 20" wheels and 245/35 front tires and 295/30 rears. 8.5"front/11.0" rear widths. I am learning that going to smaller wheels is the way to go. What is the advantage of that? Not sure if it is because of reduced cost or if a smaller wheel with the same tire size produces a bigger contact rubber patch. Or is it because you can put larger tires on smaller wheels? I know that in going to smaller I need to be sure that the wheel fits over calipers. 

If anyone is able to help me with this I would appreciate it. Do you have an opinion of what would be the best set up? Considering going to Toyo R888R tires as opposed to slicks.

Thanks,
Scott Wilkes