It Vibrates While just ideling

Have you replaced the fuel filter? That may be the culprit.

i have seen many strange things happen with the distrib cabs on these

indicates a dirty injector
cheap try is a couple of cans of quality injector cleaner and have the fault codes read by an accredited service center

Have you checked fuel pressure?
Vac leaks ?
Restriction in the air intake ? Faulty EGR valve ?

These cars tend to have bad spark plug wires, they will arc where the boot goes down into the valve cover.Check to make sure there is no oil in the spark plug well,if the is you will need to replace valve cover gasket and orings.Souds like you need a new set of plugs and wires.Look for corosion where the wires connect to distributor also as you may also need a new cap and or coil.

I would think, most likely the shocks are bad. The springs could be weak, but I would think it would sit a bit low. I'd check the stabilizer links. The vibration could be a bad universal joint in the driveshaft. I'd replace the shocks first.

Check the intake hose to make sure that it doesn't have a whole in it also check the air box that the filter goes in also. Mine was idling rough also and we found a whole in the filter box and the intake hose had a whole in it. Hope this helps.

Vacume leak or bad idle motor. With the car in park and running with the hood open listen for leaks moving your hand around the different hoses looking for a change in the sounds that you hear. The idel motor also makes the car idel up to 1500 RPM or so right at start-up then idel down, If it doesn;t the idel motor is likly. Check engine light is on when running? Test for codes, Follow code test charts don't skip any steps!.

you might want to replace the plug end. I had a 99 neon with the same ploblem changed the sensor but the plug was shorted, changed that and it run great ever since.

CHANGE FUEL FILTER CHECK YOUR UPPER AND LOWER INTAKE GASKETS OR THROTTLE POSITION SENSOR