Could be something in the tires, assuming they are balanced correctly how is the ware on them? maybe they are just worn unevenly. rotate them and see if it changes how the car feels.
if it is a bushing causing your problem, its most likely the tension rod bushing, which is the arm connecting the lower control arm to the car. If they have never been replaced on an s13 then they are probably shot. After you sort out the tire problems, you could look into replacing them,
http://www.pdm-racing.com caries whiteline urethane bushings (they even sell the control arm with the bushing already pressed in). or you could go a step up and get a tension rod from spl (
www.splparts.com) or another company. If you have a torque wrench they are easy installs, if you plan on getting the bushings pressed in...i cant remember what it cost me to get my LCA bushings installed, but maybe an hour to an hour and a half of labor per side assuming the two installs are comparable.
If you do find that this bushing is your problem (you can usually notice a bad tension rod bushing under hard braking) then i would recomend the spl tension rod, they even have install instructions on their web page. You will need an alignment after you install these though.
I have pretty much replaced everything on my front end to solve the problems ive had, and it still left an uneven feeling, and now ive found out i have bad spindle bearings, so im getting those replaced...just another suggestion, but i dont notice actual shaking, but something close to a pull.