I just plugged the quarter car transfer function you derived into MATLAB. The constants are mostly guesses, so let me know what needs to be changed. One thing that seems weird to me is that the step response has a final value of zero when I think it should be one.
edit - 'unsprung weight' should be 'unsprung mass' and 'tire spring weight' should be 'tire spring rate'
http://i.imgur.com/osZSMGs.png