As Brew said, if money isn’t an option (but in actuality it is, because if it wasn’t an option we wouldn’t be talking about modifying a Cobalt), get a new platform like a BMW M3.
Some times you gotta realize you can’t polish a turd. I used to heavily track my Subaru Legacy, but that car started to hit a dead end when I realized no high-end suspension manufacturers made suspension setups for the car. Then I switched to a car that had a much better aftermarket track following and the world has been better since.
Keep in mind when I say high-end, I am talking $2,500+ for just a set of dampers, meaning no mounts or springs included. I’m talking companies like JRZ, Moton, Motion Control, Penske, AST, etc… Bilstien, KW, Ohlins, etc… are not even high-end in my book.
With all that said, you will not be tearing anything up on the street since there’s only so much a street car could do, and that is even less when it’s a FWD car like the Cobalt. Get a new platform before dumping a cent into the car. You want to make your front engined, FWD car handle like a rear engined, RWD car. It’s not going to happen unless you’re in reverse.