If you have not already done so, take a look through our 2012 Project Car thread because I am consistently amazed at how well the Progress Spring and Sway combo works. Nonetheless, coilovers like our choices from TEIN and OHLINS are on an entirely different level of performance and if a track day once or twice a year are in the mix then I would include coilovers.
My suggested shopping list for $3000 and the goals outlined in your post includes TWO big ticket items, one transforms the handling, the other transforms the torque and sound:Roadstersport Street Exhaust combo.
That's the Street Header, Midpipe, and Q Muffler. That's what we have on my wife's 2012 and she loves the extra power and sound, just enough additional attitude that she makes excuses to drive it and give it more throttle. Be sure to watch the brief video sample at the bottom of the product listing at the link above to get just a little taste of the very mild sound (if had not turned the stereo off you might not even notice). Now if the track day was going to be more than once or twice a year I would step up to our RoadsterSport Max Power Header Combo
or our PPE Long Tube Header and Midpipe
with Q muffler....both will give you a result with even more torque but both will also give you quite a bit more sound. Every choice is a tradeoff.TEIN COILOVERS
. This might be more firm than you want for daily driving. If you decide the coilovers are more serious than you want for the daily ride, then Koni Shocks, Progress Springs and our Racing Beat Sways is my suggestion for MUCH better than stock handling with a ride that is still more plush than most sports cars from the factory.