Shaking
Brake Rotors
Over tightening the wheels lugs can cause steering vibrations at speeed, and may warp the front disc brake rotors, causing “shimmy” or shaking in the front end. This was a particular problem with 1985-1987 models. Use a torque wrench to tighten to 76 ft/lbs when tightening lug bolts on these cars. Brake discs warp most often when the car is brought to a standstill from a high speed and then kept stationary on the brake for a while. As the rest of the disc is able to cool, the area under contact from the hot pads remains heated and this difference in temperature starts to warp the disc. If the steering wobble is much worse under braking it could well be this.
Your local tire shop will probably not use a torque wrench. Rebalancing the tires will not correct this shimmy. Dealers have previously recommended purchasing new wheels, blaming aftermarket wheels, bad discs, etc. Retorque the nuts, it should help.
Balancing
Wheel balancing, is pretty cheap to have done, and may cure vibrations.
Hub-centric Rings
Aftermarket wheels likely need accommodating hub-centric rings installed. Most aftermarket wheels have a loose fit to be compatible with many makes and models of cars. Hub-centric rings widen the mating piece of your hub to have an exact fit with your wheel, making sure that the wheel’s axis is aligned with the hub’s axis.
Worn Tires
Worn tires can cause poor handling, braking, and vibrations at speed. Easy to check, but less easy to cure.