If by "weekends" you mean "at the track", then it would be far better to get a real track car, or still better a real race car, than an M3. The M3 is going to get beat up on the track, you'll be in mod-hell trying to make it into a "real" track car (don't kid yourself into thinking that any M-car is a real track car out-of-the-box), and you'll be limited to doing things like DEs where street cars are okay.
If the guesses of a $20k difference between a 335i and a M3 are correct, you could get a very good SCCA or NASA legal race car and run several events, including tires, fuel, repairs, etc. Get a Spec Miata for anywhere from $5k to $15k for a nice one, get your SCCA license, and go racing! I can assure you it's a hell of a lot more fun than DEs, open track days, canyon blasting, or drag racing. I went through the progression and ended up competing in the SPEED World Challenge last year, and my only regret is that I didn't get into racing a long, long time ago!
"Better a racer for a day than a spectator for life"
Now an M3 for the week and a racecar for the weekend would also be nice, although I'd bet on the 335i being a nicer car on the street and would rather use the $20k or so on racing.