I read through this topic, now 3 pages or more back, and decided to join the forum. Rather than bring it up to the top again, I'll start a new thread. It's a subject I've been interested in for the last 40 years.
Before beginning the beauty contest, here are my rules:
1. Size. If I can't read LIBERTY without a magnifying glass, the coin is too small. Since my eyes have gotten weaker over the last 40 years, this rules out anything smaller than a quarter. Despite their good designs I exclude
Mercury dimes,
Buffalo nickels and incuse gold Indians.
2. Represent. Liberty has to look the part. This excludes Morgan's hefty beauty, as well as the 20th century statues on the SLQ and the St. Gaudens (both of which remind me of a manatee, if it were capable of standing).
3. Age appropriate appearance. A coin is money first and foremost, and that's a part of the beauty. If it didn't circulate, or its appearance is altered, it's not a coin. It's a medallion. This rule excludes mint state coins, commemoratives, polished, dipped and damaged coins. My ideal is a coin which shows all its devices (usually VF-AU), but which also shows grime and tarnish from age. Generally it takes pre-1935 mintage to develop this appearance.
And here are my winners:
1. 1793-95 large cents. These are the best of the best. A lean Liberty, face to the wind with her hair streaming behind. A defiant liberty pole set like a spear, topped with the flag-like liberty cap. On the reverse a crude wreath (or even better on the 1793, a linked chain). Money created ex-nihilo in the form of a CENT. You get the effect as a silhouette even on a G, but it looks best on a chocolate-toned F or better.
2. Well-struck
Peace dollars. Almost as good as the cent. Liberty has the same wild untamed hair, with a facial expression of gasping surprise. The key is finding coins with well-defined hair above the ear, with a little oxidation and grime to make the hair stand out. The best appearance is on a fully-struck 1921, with the deep dish-like relief, but impressive examples are found more easily on 1925-P and 1926-P in XF-AU. The surface is important to the coin's look: it is hard to see the hair detail on a "blast white" specimen. And if it's not very sharply struck, Liberty looks like she has a bad perm and the mumps. Oftentimes MS67's look no better than a VF on this coin.
3. 1916-1921 Walkers. The most dynamic Liberty, striding confidently like Marianne on the French coins. The deep-dish of the early dates sets her off well. On the reverse the best of American eagles. You need a grimy VF or better to mske the intricate feather detail stand out.
4. 1907 NM $10 Indian. The warbonnet, and the surprised look on Liberty's face, and the font used for the date, do it for me. But what I really like is the tall reverse rim, not seen on the later dates. It creates a sense of depth and shelter, especially at the top of the coin.
These are not necessarily my favorite coins, for which I have a few more criteria, but many of them are near the top of the list. It's a lot easier to like a coin if it's pretty.