1998 Chevy Cavalier

It sound like you may have a bad motor mount. Is the car idling normally? If it is have a helper sit in the car with the emergency brake on and the wheels chocked and put the car in drive with their foot firmly placed on the brake pedal. Give the car a little gas and see if the motor jerks put the car in reverse and do the same thing. A little movement is normal but if it is moving a lot try to pinpoint which mount is allowing the movement. If the car is idling too high you will get a bang when putting it in gear. You will need to address that problem 1st.