I picked Theodore Roosevelt because he put America in the world spotlight.
Not just that: he engineered the transformation of the US to a modern world power, and was the architect of the modern model of a powerful chief executive. His reforms to provide a better way of life (see, for example, the FDA) for the average citizen, while maintaining a positive climate for business should serve as the prototype for all presidents.
My ranking:
1. TR
2. Ike (he kept a cool head during the worst of the cold war, and paved the way for the future downfall of the Soviet bloc)
3. Reagan
4. Truman
5. FDR (don't forget, there was a sharp recession in 1938 that his policies didn't do much to mitigate)
6. Ford (healing after the Watergate crisis)
7. Kennedy (+rep for winning on brinksmanship but -rep for taking the world to the brink in the first place)
8. Bush the Elder
9. Coolidge (something of an enigma [thank you, Robert Sobel] who might have done some fine things had he not suffered from depression after his son's death)
10. Taft
11. Clinton (a feel-good type who reaped the benefits of much done by Bush; should have sold used cars or real estate)
12. Hoover (authored reforms to end the depression, many of which were simply co-opted by FDR; lousy communicator, though)
13. Wilson (vastly overrated)
14. Johnson (master flim-flam man who committed the US to involvement in a messy guerilla war)
15. Harding (in over his head and he knew it)
16. Carter (in over his head but too stubborn to admit it; in some ways, the US is still cleaning messes from his naivete)
Nixon is not on the list since he's a special case: we'll always wonder what might have been without Watergate. One has to give credit for normalizing relations with China and for the real beginnings of detente, but all of that is overshadowed by Watergate itself.
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