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I only want to exclude Descartes as I have read everything he's written many times over as he's my favorite philosopher (if one is allowed such a silly thing).

While I understand that reading by myself is hardly a substitute for a degree in it, I imagine that PhD programs have an obligatory reading list.

Which books must one read?

I don't have a PhD, and my education in Phil of Mind is from self reading -- so this is my own particular list:

The best starting point I consider to be Susan Blackmore's A Very Short Introduction to Consciousness. It is packed with empirical data, and is both VERY short, and very clearly written. It provides a dialog between materialists, delusionists, and dualists as she walks one through the data. She has a preferred solution -- delusionism -- but does not make this an overwheming bias to the book. She is a devoteee of Dennett, but is a much less obscure writer than Dennett -- so this also provides a useful primer to understand where Dennett is coming from.

For Daniel Dennett, I have only read Consciosness Explained. He has a more recent version of his thinking, which apparently moderates his views a bit, I think it is Content and Consciousness. Bacteria to Bach could also be appropriate, not sure as I have not read either. You need to read one of these. Dennett is the strongest thinker on consciousness I have found in the field, and his views are something you need to understand. Dennett advocates delusionism -- that we are not conscious -- and this is somehow a delusion inserted in our memory to creat narrative consistency. Delusionism is still a small minority position despite his intellect, but an IMPORTANT minority position. The observations he cites to support it -- that we are often mistaken about what we think and experience -- is something that all mind theories need to take account of.

Another important minority position is that of Paul Churchland. I have only read one of his books, The Engine of Reason, the Seat of the Soul. He is a neuro-reductionist, and tries in that book to show that consciousness is simply the operation of recursive neural nets. Another author who takes the same approach is Francis Crick's The Astonishing Hypothesis. You need to read a good neural net reductionist, either of these would do. Neuro reductionism does not convince most people, as it dismisses qualia entirely as irrelevant, but this is an important view, and even if you don't accept it, there is a great deal to learn from the neural net behavior of our brains.

John Searle is a pretty important counter thinker to read. He critiques and rejects the two reductionist/delusionist views above. I have read The Mystery of Consciousness -- which critiqued materialists, but did not offer his own model. He has written a half dozen other books, not sure which one you should go for, but you need to read him.

Another important one -- Karl Popper and John Eccles -- The Self and its Brain. Spells out why all forms of materialism that are not strongly emergent property dualism are refuted by observations and evolution, and makes a case for emergence, and for interactive dualism. The author of our current scientific method, teaming with a nobel prizewinning neurologist, make a pretty strong case to treat dualism more seriosuly than most other thinkers today do.

The final two are not philosophy books, but more evidence based.

Thinking Fast and Thinking Slow, by Daniel Kahneman, is an outstanding discussion of the details of how we actually think, and how we seem to have two very different kinds of modules in our mind. It comes out of his decades of study of social psychology and decision making. The Man Who Mistook His Wife for a Hat by Oliver Sacks are case studies from a clinical neurologist detailing how brain damage took pieces of selfhood away from his patients. These two books show the "unity of consciousness" assumption, intrinsic to much philosophy of mind thinking, to be absurdly untrue.

This is my core reading recommendation. There are a lot of writings all over the place in philosophy of mind, and I expect you will get very different recommendations than these from others.