Welcome Steve,

The sound and feeling you describe is probably the ABS (antilock brake system) activating. I notice it in my '88 260e only if the rotors are wet (like when the car sits outside overnight), or a tire is low. My wife's '92 300e seems to do it one every time the car is started. Either way, I think it is normal but you may want to verify your tire pressure and make sure all your tires are the same size. The ABS system senses if the wheels are rotating a different speeds with bad tires may not operate correctly.

John