Chaimv,
Welcome to the Stovebolt. Many Canadians are kicking around here so you shouldn't feel lonely.
Finding your vibration might take some sort of special tools. A compression check with a gauge would be a good starting point.
I am thinking your vibration might actually be a 'shaking' from a cylinder that isn't firing properly.
If you get a chance, next time it does the vibrating thing, pull each plug wire, one at a time. Most should make a big difference when removed..if one doesn't make a big difference, you might have found the culprit.
If this vibration is actually a shaking of the engine, this miss could also be caused by faulty plug wires, bad distributor cap, or a valve malfunction.
If your car turns over nicely when warm, but won't start, it could be a fuel issue.
Sometimes a carburetor will percolate fuel into the intake after the engine is shut off. This can flood the rig and make it hard to start. Black smoke out the pipe on start up would be a clue.
There are many things to look at for a sure cure. The comment on the vibration could be something entirely different than I indicated.
I called it a shaking of the motor, you might mean a subtle vibration. This would be different.
Other folks will soon be along with more ideas.
Stuart