This sounds like my car exactly.
I just bought a 1999 323i bimmer and I'm having nothing but problems.
I have the same issue as the OP, when I start my car after its been off for a while it shakes 5-10 times more than normal.
I give it gas and have no power. Car jerks and the problem seems to go away if I turn off my car and start it back up a few times.
Other problem I notice is that my car wont do donuts. I rev my engine, pop it in first gear, and my car sounds like its about to break so I quickly hit the clutch pedal. Anyone know whats the problem? I should be able to do donuts no problem in a bimmer!
Other issues my car has is the driver side Halo lights don't work properly, my instrument cluster buttons don't work. I can't set the clock or reset the trip odometer.
Also my car seems to be loud but I'm not sure if its suppose to natural sound that way or not.
I just ordered a Service Manual for my car to help me figure some of my issues out.
IF anyone knows any solutions to my problems, I will be grateful!!!!