Who comes first in both of these categories?
"Mentioned either as best or worst".

Abraham Linkon as the best

I can't find the worst though

edit post: I found this website with a list of 10 best and 5 worst, but I don't know if this website can be counted as official.

Who would you rank the best and worst U.S. President?

Top 10 Best U.S. Presidents

1. Abraham Lincoln
2. George Washington
3. Franklin Delano Roosevelt
4. Thomas Jefferson
5. Theodore Roosevelt
6. Harry S. Truman
7. Andrew Jackson
8. Woodrow Wilson
9. Dwight David Eisenhower
10. Lyndon Baines Johnson

Top 5 Worst U.S. Presidents

1. James Buchanan
2. Warren Harding
3. Andrew Johnson
4. Franklin Pierce
5. Richard Milhouse Nixon

http://boards.biography.com/forum.jspa?forumID=434

The person I am looking for is the most mentionned as either best or worst. Since the study was done in 1999 G.W Bush is not competing here, and the poll was conducted by a university in Illinois.

http://sro.uis.edu/Presidents.htm

Most Frequently Mentioned Presidents:

Mentioned either as best or worst.
Bill Clinton 39%
Ronald Reagan 27%
Franklin D. Roosevelt 23%
Richard M. Nixon 23%
John F. Kennedy 14%
Jimmy Carter 13%
George H. W. Bush 8%
Harry S Truman 6%
Dwight D. Eisenhower 5%
Herbert Hoover 4%
Lyndon B. Johnson 4%
Gerald R. Ford 4%

Got it! Bill Clinton.

The results of polls like this change, of course, depending on who's asked and where the asking takes place, and, of course, with time. AT one time, FDR would have won a national poll for both best and worst. Then it was Nixon. I saw several with Reagan in that role. Now it is Clinton, and in a few years, it will surely be W.