94 Taurus engine shake after starting.

What size engine? 3.0 or 3.8? Motor mounts will usually not cause shaking, to check for a broken mount either put it in park, hold the brake pedal and slightly rev the engine, there will be a definite thump if there's a problem. Or better yet have someone observe the engine, make sure not standing in front of the vehicle, while you do the same park, brake rev deal. The engine will lift up pretty good with a bad mount. If you have the 3.8, I wouldn't wish that motor on anyone, they are notorious for busting motor mounts, weak design combined with big torque, and the worst thing is, no one has improved the mount to where it's reliable in the long haul. You live in an area where snow and ice are common, you spin your wheels even a little bit, then grab a piece of dry pavement you're looking at a broken mount, I want to say the right front is mostly the culprit, not 100% on that though

I'd throw open the hood and check all wiring, vacuum lines, etc make sure nothing has been knocked loose, any work done on it lately? Check the sparkplug wires, make sure they're tight. Might be time for a tune-up, new plugs and wires, also important take your distributor cap off, I would almost guarantee there's corrosion inside on the rotor tip and the contacts on the cap itself, replace the cap and rotor with new if not done recently, make sure you get a little tube of dielectric grease to lightly coat the rotor and cap contacts, you need the grease for the sparkplug tips and wire boots anyway, then regularly check the cap and rotor for buildup. Also as usual I recommend you get yourself a code reader for your car, around 30 bucks, and learn how to use it, not hard. Could be throwing a code and not setting the check engine light.

Gap for plugs should be on the radiator sight shield, that label would also include the vacuum routing diagram, I think it's 052-056. I would use either Motorcraft which is oem or Autolites also have worked fine for me. Are you familiar with doing the fuel filter?