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I just put some Max Performance Sumitomo HTRZ III's on the car, so I should be covered in the tire area.
FYI, those are several generations old and were never considered a competitive tire even when new. They aren't *bad* tires and are fine for typical street driving, but they aren't comparable to a modern extreme performance tire. Tires are the only thing that will determine stopping distance for this car. Brake upgrades only affect how the car handles prolonged, repeated abuse. Even for that, as others have mentioned, just focus on pads until you start cracking rotors.