I think a pretty fair case can be made that the U.S. does a terrible job picking who to put on our money. First of all, we have repeats - Lincoln on the penny and the $5 bill; Washington on the quarter and the $1 bill; Jefferson on the nickel and the$2 bill. Second, if you really want to honor the most important people in our history, we've way overrepresented Presidents (particularly when you consider the duplicates) and we've way overrepresented people born before 1800 (Washington, Jefferson, Hamilton, Jackson, Franklin), at least on denominations that get used regularly.
Personally, I would go for the idea of setting the penny, quarter, $1 bill and $5 bill permanently to honor Washington and Lincoln as the two most important Presidents, and then changing all of the other bills every ten years or so to honor other important people, and particularly non-politicians. Truth be told, the suffragists are as important in our history as Jackson (probably more so), and we simply don't honor people like Alexander Graham Bell or the Wright Brothers who were responsible for significant advances in our society. It would be great to do that.