There are three causes for steering shake under braking, although one is disputed by the experts:
1. warped rotors (disputed)
2. brake dust deposits on rotors
3. worn or loose front control arm bushings

On the warped rotor debate I am on the side of the skeptics. Much has been written that support that position from people who should know. One exception is warped rotors as the result of extremely tight lug nuts. That leaves 2 and 3.

Certain brake pad types are more prone to dust deposit build up. I'll be curious to know what brands people are using with kind of results. Typically OEM is the safe choice.

On the control arm bushings, the lower (rear) is often the culprit. And it is not so much that the bushings wear out but more often the nuts that hold the bolts in place loosen up and allow movement inside the subframe. Together with dust deposits on rotors, this will result in the dreaded shake. These need to be torqued at around 74 lbs-ft if I remember correctly. This is often overlooked but easy enough to check.