There's more to it than has been mentioned so far. "Seat time/driver mod, wheels & tires, everything else" is the general order of where the biggest improvements come from (at least as measured by autocross run times and road course lap times).
Anyway, you'll want wider wheels and tires than the GT/PP comes with. More like what the non-R GT350's come with would be a start, though with big power you might need a little stagger. "A little" is no more than 20mm front to rear tire size difference or 1.0" width difference in the wheel. More difference than that in a front engine/RWD car is normally reserved for appearance-only mod programs and drag racing.
Then there's the matter of seat time . . . but I'd urge you to get some seat time at autocross and HPDE even before proceeding very far with your car mod program. It can help you understand better what the car needs to make it better for you for the hard driving part. You might discover things that don't get fixed with stiffer springs and bars or better shocks. Right now, I'm having to assume that you're going to drive this thing pretty damn hard from time to time (hopefully on a road course).
For instance, there's a lot of compliance in the IRS that compromises away precision in the name of softer ride quality. BMR does have a number of IRS components that address this part of handling goodness (camber links, vertical links, cradle/diff bushings, and toe rods), and there is an aftermarket upper rear shock mount that is said to provide much better behavior as well (I'm not sure offhand whose these are, maybe they're Steeda's?).
'08 GT coupe, 5M, wheels, tires, pads, fluid, a few suspension mods . . . still almost stock height
'10 Legacy 2.5GT, 6M (hers)
'01 Maxima 20AE, 5M (spare, winter driver)