I think @NyssaUnbound has read a few more than me (I’ve read up to The Adventuress of Henrietta Street), but I can definitely give a rundown up to that point of the most plot-relevant & beloved books.
I’ve meaning to write something like this for a while, so prepare for a long post…
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I think almost everyone agrees Vampire Science is the best place to start. You do not need the context of The Eight Doctors to understand who Sam (the Doctor’s companion, a teenager from Coal Hill School in the 90s) is, and it’s a fantastic book too. The Eight Doctors is… not particular liked.
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Alien Bodies is extremely important to the plot, and very highly regarded too.
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Longest Day, Dreamstone Moon and Seeing I form a three-book arc. I’d say you could jump in on Seeing I (which is a brilliant book) without the other two, but I also like Dreamstone Moon quite a lot. Longest Day is more controversial.
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The Scarlet Empress introduces Iris Wildthyme to the range and is a joy
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The Taint is… not a good book IMO but it introduces Fitz, who is a much-beloved character!
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Revolution Man develops Sam, Fitz and the Doctor very well.
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Unnatural History and Interference books 1 and 2 are essential and fantastic.
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The Blue Angel might not be strictly essential but it IS essential To Me. And it’s beautiful.
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It’s also part of a long-ish arc where 8, Fitz and Compassion travel together; I’d recommend reading them all probably but The Taking of Planet 5, The Shadows of Avalon, The Fall of Yquatine and The Ancestor Cell are definitely essential.
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The Earth Arc (spoiled for a reason!) is in a weird place where most of the books are essential-ish for the arc but they could also be read without any prior reading. That’s The Burning, Casualties of War, The Turing Test, Endgame, Father Time and Escape Velocity. (The first three books are really good IMO, The Turing Test being one of the range’s best; the last three are, again in my opinion, pretty bad, Father Time especially, through I’m in the minority there.)
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The post-Earth Arc is generally considered the “golden age” of the range; Earthworld and Eater of Wasps are generally liked, and The Year of Intelligent Tigers and The City of the Dead are ADORED. Tigers is a lot of people’s favourite Who book, including mine. I also really like Grimm Reality!
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The Adventuress of Henrietta Street is the start of another arc featuring Sabbath; I’m only at the beginning of this one so I can’t say for certain, but I’ve heard most of the books if not all from this point on follow on quite strongly from one another.
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There’s also Fear Itself, which is technically a PDA but features 8, Fitz and Anji, and is also strongly loved.
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