Idle-only vs. all-the-time
If the shake disappears once you start moving, the cause list is short and mostly inexpensive.
A rough idle that smooths out at speed usually points to spark plugs, engine mounts, or a vacuum leak.
Only at idle / stop lights
Felt through the whole car
Textbook sign of one or two plugs misfiring only under light load.
Deteriorated mounts let engine vibration transfer into the cabin.
Destabilizes idle speed specifically.
If the shake disappears once you start moving, the cause list is short and mostly inexpensive.