My poll and reason for including them would be:
Washington - The first and he set the tone for the position
Lincoln - Waged a bloody civil war to prevent the Confederate States from leaving the country
Franklin Roosevelt - Brought the country out of the depression and partly through WW2
Reagan - Restored hope after the catastrophic malaise of the Carter presidency.

Unfortunately, with the state of public education in the United States, most younger people probably know next to nothing about any of them.