Make sure your rotors are not warped and properly installed. If the shaking only happens when you brake, make sure your caliper bushings are not ripped and your rotors are bolted in. I had that problem on an E36 and we changed the rotors, problem solved.
As far as the thudding goes, make sure your strut mounts are in decent shape. Also check the balljoints and tie-rods, very common failure item on many generations of BMW's. The thudding is most likely a product of worn out suspension items that now have a lot of slack.