I've taken my 100% stock E93 on three track days this year.
Each time I've gotten better lap times.
Until you've bottomed-out and aren't making any improvements, why spend any money for modifications
At the last track day, I learned enough about the car to start wondering what would be next:
I can tell you, though, that it will be track-only tires. I have 16,000 miles on my 18" wheels and the wear-bars are now flat-on the tire. Basically, they're done. These were Mich PS2's.
Fortunately, previously I bought a set of spare set of 19" wheels/tires, and those are the daily driver as of last week; and I'll buy track-only tires for next season and toss those on the 18" wheels.
So my relatively-inexperienced advise is: keep it stock until you can't get better times; and then get ready to spend money on tires.
Just go have fun!