There’s no better way to get better at driving than doing an HPDE (driver’s school) on a real track. Get a BMWCCA membership, sign up for an event. Don’t waste money buying parts that you think the car needs to handle better or what not. At a track, the only thing you need is safety and brakes. I’ve seen guys on track with some jalopies, such as a newish Ford Five Hundred. I’ll let you think about that for a moment and let it sink in… A Ford… Five Hundred… On track.
As Brett said earlier and Jeff also just said, brake fluid is important as well. For any street car, ATE superblue is perfectly fine and has a high enough wet/dry boiling point. Once you really start using the brakes, which I can promise you will never happen on any mountain road or street, jump to Motul or something more expensive with even higher boiling points.