Lol, funnily enough I went through a lot of these on what i thought was "my own initiative", that is, without ever seeing this chart. I guess I'm less original than I think lol.
Can personally vouch for Manly P. Hall as a very good primer, and Gurdjieff and Ouspensky as good "big-boy stuff"
Not too big on the Golden Dawn stuff and Kabalism, there's maybe nuggets of knowledge in there but a lot of it is masturbation over esoteric concepts that they probably don't fully understand and that you need to know Hebrew to get, lol. Especially not too big on Crowley, a very turgid writer and i accuse him of the same thing --- writing about stuff he probably doesn't know about, but just seems poetic and cool to him. Some Egyptian mythology here, some Qabala there, some trappings of Eliphas Levi and Hermeticism there, etc., etc...
Robert Anton Wilson is a good intro to the whole subject, despite what other people say. A good INTRO. The more you get into it, the more you'll disregard what excited you so much in the beginning. I'm saying this in the same way that I wouldn't suggest, say, Finnegans Wake to someone who wants to get into literature.
Also Huxley (Perennial Philosophy) and Joseph Campbell (Hero W/ A Thousand Faces) could be good intros.
In general, start with the stuff that interests you to feel around and have an understanding of basic concepts that will be repeated again and again in occultism, you shouldn't dive straight into even Crowley (who I don't like but at least admit writes in a very complex, nuanced, allusive way at times).
Gurdjieff and Ouspensky (from what I've read of the books there) are probably the most mindfucking writers IF they touch something in you. If they don't, then count yourself lucky, as you won't be tortured by obsession with them. I' surprised In Search of the Miraculous isn't on that
The Kybalion also is great and could be read whenever you want, hard to call it either a beginner or an end-level book.
All in all, use, to the degree you can, your own judgement and read what interests you. You don't have to listen to me or anyone else (can you trust me as a genius or a sage?), and if you don't start off with reading what may be trite but interesting, you won't be able to build up to more complex books on it. Just cause I dislike what the Western tradition has of Hermeticism and Theosophy and all that blend of stuff doesn't mean you shouldn't read it, in fact I insist you SHOULD read it to go through the same process i did --- taking what's good from it, and ultimately realizing what stuff you can throw out based on your judgment. There are seeds of great and beautiful knowledge in them from what I know.
Also is a good post.