You may want to read "The Contrarian's Guide to Leadership" by Steven Sample, a book which proposes the theory that reading the books of ancient literature is a superior way to gain managerial skills than immersing oneself in day to day newspapers and pop lit. Ironically, the book is itself a piece of pop lit so you may want to take all this with a grain of salt. :) He argues in ch 4 of his book that the ability of great American presidents in the past to lead the country so well was based on the fact that they were products of the literary culture that you're describing. The book is also didactic, so it would satisfy your criterium of being a manual for self instruction.

If you would like a more traditional experience I urge you to check out the series "Great Books of the Western World" and read the foreword.

http://www.nytimes.com/2008/11/16/books/review/Campbell-t.html?pagewanted=all&_r=0

Are you interested in the general Enlightenment culture which would have informed the early American leaders' thinking, as well?

Basically, what you are looking at is a Classical Education. While you can get this at any college/university that has a Classics Program, I don't believe that you are able to go through this.

Basically what can be recommended is classical languages. Ancient Greek and Latin form the corner stone of any Classics program and it is very possible to teach yourself these classical languages. The books I would recommend are Whelocks, a Latin book that I used in a self-paced Latin class; and Athenaze, a book series that focuses on teaching Attic Greek (the main form of Greek as there were several dialects).

Other than that, all I could recommend is reading a lot of Ancient philosophy, particularly Cicero.

Not sure of books, but The Teaching Company has a number of courses that tackle the subject of classical Greek literature. I know that at least some discuss the material in the framework of it's importance to Americans and Englishmen as part of standard higher education.

I think that Masterpieces of Ancient Greek Literature by David J. Schenker would interest you in particular, but there are at least 3 or 4 others that might strike your fancy.

I wouldn't recommend using 18th-century translations. For Latin, you can't go wrong with Fagles, and for Greek Lattimore is basically like reading the original. If you read the Aeneid, the Odyssey, and the Iliad, you will have a very solid classical background.

Source: two years of Greek, self-taught in Latin

I'd suggest that you pick up any fairly recent translation of Herodotus and start reading. It's pretty readable. If you like it, continue with something else. Perhaps Thucydides (starting with history may give you a bit of context when you get to literature).