The Judgement of Paris
Some questions are best avoided. When faced with three beautiful coins, it seems that asking "Which is fairest?" is perhaps not a good idea. Before I get to the coins - let's start with this hydria from ancient Greece and the British Museum.
Pottery: red-figured hydria (water-jar). Judgment of Paris. Right to left: Paris, seated on Mount Ida, in front of him, in order, Hera holding the Golden Apple of Discord, Athena with spear, Aphrodite on the far left. Copyright for this image is retained by the British Museum Trustees, used with permission under Creative Commons Attribution-Non Commercial - Share Alike 4.0 International (CC BY-NC-SA 4.0) license.
The Judgement of Paris by Sandro Botticelli, AD 1485-1488. Public domain via Wikipedia.
King Peleus and sea nymph Thetis were to marry (Note: These two are the would be parents of Achilles. Thetis the one who would hold her son by his heel as she dipped him in the River Styx to confer invulnerability). The party was the talk of the town. Eris, uninvited, and upset, so she threw a golden apple amongst the wedding party. On the apple were the words, “To the Fairest”. After a bit of a scramble for the apple, Zeus, wise enough to know that he didn't want to be in the middle, assigned to Paris, the Trojan prince, the task of awarding the prize.
Here is how Helen tells the story with the words of Euripides (Note: Aphrodite was also called by some Kypris in honor of her birth off the coast of Cyprus).
"My name is Helen; I will tell the evils I have suffered. For the sake of beauty, three goddesses came to a deep valley on Mount Ida, to Paris: Hera and Kypris, and the virgin daughter of Zeus [Athena], wishing to have the judgment of their loveliness decided. Kypris offered my beauty, if misfortune is beautiful, for Paris to marry, and so she won. Paris, the shepherd of Ida, left his ox-stalls and came to Sparta, to have me in marriage." - Euripides, Helen, translated by E. P. Coleridge, 1938
I think it prudent to leave this post without awarding the golden apple - it didn't end well for Paris. His selection and the promise of Helen was the start of the Trojan War. In the end, he stood on the wrong side of arrows from Philoctetes (at least by one account). Here are the three goddesses in no particular order:
Hera (Pontus) 400-360 BC
Athena (Akarnania) 350-300 BC
Venus (Rome) 81 BC