To simplify matters, I will just list the suggestions Oliver Van DeMille makes for each topic of study. Remember, as the student reads a book, the parent/teacher should be reading it at the same time. If it is truly a classic, having stood the test of time, it is worth reading over and over again, even if you have several children or if you are teaching it year after year! Also, most of what I will list is the authors who wrote classics – many of them have many books for you to read.
Literary Classics: The Bible, Shakespeare, Dickens, Austen
History Classics: Plutarch, Gibbon, Toynbee, Durant, Declaration of Independence, original documents from various time periods
Math Focuses: There are 13 skills which Van DeMille says a student will learn from the math classics: seek and recognize patterns, explore the relationship between things, see similarities and distinctions, analyze logically but with a deep sense that there is a right answer and a set ideal worth detecting, compare and contrast, see things in black and white, see infinite shades of grey and therefore avoid jumping to conclusions, seek evidence for conclusions and check opinion with first-hand research, put his own pen to paper before accepting what society tells him, seek for absolutes, and remain open to surprising new information which makes past conclusions limited though perhaps still accurate
Math Classics: Archimedes, Descartes, Newton, Sophie Germain, Einstein, Euclid, Newton
Science Classics: Copernicus, Galileo, Agassiz, Einstein, Darwin (even if you disagree with an author, find out about them! You might find that you know them better than those who say they support them, and they may not even be saying what you have heard they say!)
Foreign Languages: Read classic literature that you have already read (see Literary Classics) in the language you want to learn. Read the Bible or Shakespeare in the other foreign language, with English side-by-side with the new language. Also, have 2 dictionaries – a translation dictionary and a dictionary fully in the other language.
“The Arts” Classics: Study the Masters of that medium (Music, Art, Sculpture, etc.). Read biographies, as well as study the medium the master used.
Business Classics: Peter Drucker, Edward Demming, Stephen Covey
Government Classics: Locke, Madison, Tocqueville
Psychology Classics: William James, Freud, Skinner
Biology Classics: Hippocrates, Agassiz, Darwin
Since many of these books can be expensive, I recommend you begin with books found in your local public library. I am sure you will need to purchase at least some of these books, but begin with what you can find locally for free.