Explanation of the different parts of a BMW E36 suspension and a basic diagnosis of problems that you may have with your suspension.

Examine all bushings, paying close attention to cracks in the rubber. Look for cracks and/or grease escaping the sway bar link. 

Lots of play in the tire could point to a bad tie rod and/or control arm.

Just press down on the car to examine shocks and struts, if the car  bounces a lot than the shocks and/or struts are blown.

Suspension diagnosis on a BMW E36 is rather easier and relatively quick to do.