This is a tough question. Which of these men (Tyler, Fillmore, Johnson, Arthur) was the best when he surprisingly became President? I can make a case for three of the four. I will post the results here in a week when the poll closes.
This poll has closed and we have a tie between Tyler and Arthur. Johnson and Fillmore ran a distant third and fourth. Tyler established that a Vice-President did become the President when a vacancy in that office happened. Arthur proved to be a top notch reformer of the civil service. I can argue for Johnson too. Maybe he was not a great president but he did keep the Radical Republicans from punishing the south too harshly after the Civil War. His presidency gave people some time to cool off.