The Kosei wheels are a little narrow (17×7-in.) and the Dunlop Direzza ZII tires are a little tall and too wide (235/40R17) for Street Touring, but they'll make fine commuters and we'll replace the tires with something more comfy for street use when the Dunlops wear out.
After the driving part, the biggest factor in autocross and track performance is good tires. The STF ruleset allows 200TW tires like this newly-updated Toyo R1R and that's what we chose for our project.
The Toyo Proxes R1R that we picked for this project is a 225/45R16. Street Touring F specifiies a maximum stated treadwidth of 225mm. The shorter sidewall should help our Mazda3 accelerate, especially considering it has a very tall second gear.
An additional advantage of the Toyo's sizing is that it's about 1.7″ shorter in diameter than the stock 205/60R16, which effectively lowers the car .85 inches without any impact on suspension geometry—a win-win. Here's a quick and dirty tire size calculator that we reference often.
Toyo makes it pretty clear that the R1R is a summer-only Ultra High Performance tire, with warning labels essentially stating that all bets are off when the temps get near freezing. We've been warned.