The springs on the clutch disk normally only do this if they have been overheated. This usually includes glazing or heat cracks on the flywheel from slipping. If you go for a clutch pay special attention to the flywheel since if it is damaged, the bouncing engagement will still be there. The flywheel must be Blanchard ground or replaced if damaged.
To check motor mounts leave the hood up and have someone watch the engine for movement. Stand on the brakes and let the clutch out to load the drivetrain. It should only move about a half inch worst case.
