For George Washington I prefer either of these two...
Both were painted by Charles Wilson Peale. The first is from 1772 (pre-Revolution) and features Washington in his Virginia militia uniform, the second was painted in 1776 and features Washington in his Continental Army uniform.
The portrait from the first page of this thread is probably more familiar to most people since it is a close match for Washington's image on the $1.00 bill, but it was painted in 1796 when Washington was nearing the end of his life. He looks quite elderly compared to the other two, which were painted when he was still in his prime. It also why I wish one of these two had been used for the U.S. dollar instead.
At the time of his inauguration, Washington only had two of his own teeth left. As he aged, there was a distinctive hollowing of the cheeks in his appearance and later signs of bone erosion - both basically from tooth loss.
I think that the main image they use is that one by Rembrandt Peale, Patriae Pater , which was criticized at the time it was painted of being rather flat or inauthentic... he painted it from other likenesses of Washington (including his father's - Charles Wilson Peale - paintings) after G. W. died... I think that people like the sternness and sort of monumental/enduring/immortal aspect of the painting to represent Washington as a government figurehead... not the very living, relatable, real images from his youth.
Did you know he had red hair? LOL. He is forever remembered as an older man with white hair or white wigs as was the fashion... but he was a total ginger!