Is there any verse in the Quran that says the prophet is the best man of all time?
What do you mean by best? This egoism is contrary to the very essence of Islam. In the aya of Quran (2:285) It says we as muslims believe in all the messengers of Allah and we make no distinction between them. We cannot say that Muhammed (pbuh) is better than Eisa ibn Merriem or Musa (pbuh) or any other messenger. That being said messengers of Allah are in a class by themselves. Biologically they were just as human as we are but they are very special in that Allah has chosen them to deliver the otherwise unknowable knowledge to mankind as a mercy.
This comparison and competition in worldly matters is actually a sin and is called "takathur" and the Quran has an entire surah that addresses it; see Quran 102:all.