This isn't remotely like the other question other than it's a comprehensive list request. The other post is looking for philosophy complementary to STEM, which I would suggest is largely modern and post-modern philosophy in the analytic tradition since it is strongly tied to STEM development. This request should be satisfied with Classical, Scholastic, and Continental Philosophy. (So don't take closure personally, of course.)
You can start with books that have that theme: greatest philosophers and greatest philosophy books. While this is somewhat dictated by style, personal preference, and politics, we can serve up a few examples starting with Mauro's suggestion and following it:
- Britannica's The 100 Most Influential Philosophers of All Time (GB)
- Bertrand Russell covers a comprehensive list, though dated in his History of Western Philosophy (GB)
- My personal favorite "guide" is a set of dated and hard to obtain books called Great Books of the Western World (bookfinder.com) edited by Mortimer Adler. I'll include his list of significant philosophers below.
- The Philosophy Book: Big Ideas Simply Explained (GB) is a contemporary overview. I know you want to read the books, but it's a good overview.
You can also find lists of philosophers in the following set of encyclopedias:
- The Stanford Encyclopedia of Philosophy and it's table of contents
- The Internet Encyclopedia of Philosophy and it's table of contents
- The Routledge Encyclopedia of Philosophy (paywalled)
- The Encyclopedia of Philosophy (print)
Of course, there's a political edge to your question which used to be called the culture wars. One forceful voice that we should continue on a path of continuity with our past is Allan Bloom in his The Closing of the American Mind. I leave you with an essay about the book and its influence (s-usih.org) from the popular media. Of course, the "Western canon" is not any one standard, but a general historical preference. My views neglect philosophy of India, China, and Japan mostly out of my lack of philosophical ignorance and interest in analytical philosophy. Also, the views I present here weight antiquity, the medieval era, and modern philosophy, and neglect postmodern philosophy. There's also a modern political and stylistic distinction between the contemporary analytic and Continental activity.
Without more ado is the list of Great Books endorsed by the University of Chicago and Mortimer Adler:
- Homer
- Aeschylus
- Sophocles
- Euripides
- Aristophanes
- Herodotus
- Thucydides
- Plato
- Aristotle
- Hippocrates
- Galen
- Euclid
- Archimedes
- Apollonius
- Nicomachus
- Lucretius
- Epictetus
- Marcus Aurelius
- Virgil
- Plutarch
- Tacitus
- Ptolemy
- Copernicus
- Kepler
- Plotinus
- Augustine
- Thomas Aquinas
- Dante
- Chaucer
- Miachiavelli
- Hobbes
- Rabelias
- Montaigne
- Shakespeare
- Gilbert
- Galileo
- Harvey
- Cervantes
- Francis Bacon
- Descartes
- Spinoza
- Milton
- Pascal
- Newton
- Huygens
- Locke
- Berkeley
- Hume
- Swift
- Sterne
- Fielding
- Montesquieu
- Rousseau
- Adam Smith
- Gibbon
- Kant
- The Federalist Papers
- J. S. Mill
- Boswell
- Lavoisier
- Fourier
- Faraday
- Hegel
- Goethe
- Melville
- Darwin
- Marx
- Engels
- Tolstoy
- Dostoevsky
- William James
- Freud