HM mm - - -your question is complicated by the March of Time and peoples perceptions... In America a vast number of people call themselves a Republican and therefore any President who was not a Republican is denounced as a Socialist Traitor whose corpse ought to be disinterred and hung from a scaffold on the White House lawn while their deeds are rewritten as being misdeeds.
Therefore on the surface the Four Faces of Mount Rushmore are 'safe' choices; Washington had no Political Leanings in fact distrusted Political Parties and believed that it was Noble to Serve the CItizens of the US of A - - - and since sanctimonious Republicans think that their every deed is sacred & decreed by God they 'naturally' assume Washington was one of them.
Jefferson presents even more complicated problems. Since 'he' wrote the Declaration of Independence he had been sanctified. Any perceived misdeeds swept aside, in fact less then ten Americans can actually cite Jefferson's faults aside from 'UnGodly Liberals' who insist Jefferson fathered a child or two out of wedlock with a 'colored' slave. Since Jefferson styled him self a Democratic-Republican, modern day Republicans claim Jefferson as one of their own without knowing the irony behind their choice (Jefferson was a master politican capable of cruel conniving and not above getting Congress to cancel his debts in France through the purchase of the Lousianna Territory etc)..
Then there are the two Republicans whose image gets trotted out at election time. Lincoln and Teddy Roosevelt. Neither was a typical Republicans, in fact if Lincoln had not been assinated by bullet his fellow Republicans would have assasinated him with words & scurrilous talk. T Roosevelt was a Progressive, he became a Republican because that was the Party that he felt could carry him to prominence and through sheer force the Republians adapted a few of his policies and claimed them for themselves.
I will definitely cite Washington, begrudingly Jefferson, most loudly & proudly Lincoln and T Roosevelt as 4 among the 10 and will round out the list with several names that will anger the majority of Americans since several are Democrats; Franklin Roosevelt, Harry S Truman, Dwight Eisenhower, John F Kennedy, and since you want ten and I refuse to jump on the Reagan bandwagon, will toss in John Adams and Chester Allan Arthur.
The Worst; Geo W Bush tops the list followed by Richard M Nixon (who was, oddly enough, one of America's greatest Vice Presidents!) and then James Buchanan, Andrew Jackson, Franklin Pierce, George Senior Bush, Martin Van Buren, Millard Filmore, James Madison, and since you request 10 begrudingly James Monroe..
The sad truth is that mostly America has had mediocre yet serviceable Presidents and most likely will continue to do so.
Peace////////////\\\\\\\\\\\\\\\\\\\