I'm curious as to how the Ivies became known as the Ivies and how the schools decided who was in and who was not. They're not all the oldest schools in the US (because William and Mary and UVA aren't considered Ivies), and they weren't in a historical educational consortium together (at least, not that I know of). So how did a bunch of seemingly random Northeastern schools become known as the Ivies, and how did they come to be known as the most prestigious schools in America?
UPenn is public
It is not. The only Ivy League school with a significant public component is my alma mater, Cornell. But Cornell is a private school as well, it's just that it's considered a statutory school by the state of New York, which means that certain colleges of the school (CALS, Human Ecology, ILR, and the Vet school, as well as the now-defunct College of Forestry) receive public funding. But all members of the Ivy League are private schools.
The Ivy League is a sports league. Strictly speaking it is nothing more than that. The Ivy League schools have long had sports associations with each other. The Rowing Association of American Colleges, established in 1870, was the first collegiate athletic association in the United States. It was formed by Harvard, Bowdoin, and the Massachusetts Agricultural College (now UMass Amherst) and contained most of the later Ivy League schools. Harvard placed second in the first championship, Brown placed third, Yale boycotted, Columbia won the fourth championship, Cornell the fifth, Penn won the twelfth, and so on. Prior to this, the earliest intercollegiate sports had been largely the place of future Ivy League universities: the first American intercollegiate sports event was Yale's 1852 challenge to Harvard to a rowing race. The RAAC was disbanded in 1894 and replaced the next year with the Intercollegiate Rowing Association. Initial membership was Cornell, Columbia, and Penn: currently Navy and Syracuse are also included, and all the other Ivy League schools, while not technically part of the association, are always invited to competitions. In 1902 a basketball league was formed by Columbia, Cornell, Harvard, Yale, and Princeton, with Penn and Dartmouth joining a couple years later. And so on and so forth--sports leagues were formed, often on a temporary basis, and reformed, usually consisting of future Ivy League schools and occasionally other Northeastern universities (Army and Navy commonly were included--note that Army and Navy were very nearly added to the formal Ivy League in 1982). Schools like William and Mary or UVA have not historically been included in these associations because they are not from the Northeast.
The actual, official, Ivy League is rather recent--the Ivy League is considered to have formed officially in 1954. Before that, however, there was a 1945 Ivy Group Agreement, which set regulations for the budget and so forth of the members' football teams. And by the 1930s at the latest people were referring to an unofficial "Ivy League," and there was rumbling in the student bodies of the universities for a couple of decades that just such a league should be formed.