hey, i have a 323is, and it shakes really BAD when i first got it.
Here is my comments:
1. Is the car shaking when u reach the certain speed or shaking at the all time. If the car only shaking at certain speed, like high speed, it seems like u need to do the aliment and wheel balance and, check the tires.
2. If the car shaking under some situations, it may be the bushing and control arms. I changed my both bushings and control arms since the bushing is really bad, it cannot hold the arms anymore.
3. If the car shakes when it is idle, it seems like that u need to change the spark plug...
Anyway, check the bushing and control arms, that's maybe the reason why it shakes. The bushing is like a black circle that hold the control arms, touch it, if it is not tight, change it!