Reddit reviews Doctor Who: The Vault: Treasures from the First 50 Years

I also recommend the wiki, though if you are concerned about spoilers then you should be careful about browsing it before you catch up!

edit: As far as books are concerned: if you are interested in the behind-the-scenes story of the show, consider Doctor Who: The Vault. I own this one, it's a lovely coffee-table book that covers the production of the show from 1963 onward. (It was released for the 50th anniversary, so it unfortunately excludes any information on Capaldi's era, but still a good purchase.)

A quick Amazon search turns up this book, which may be some of what you're looking for? This is a biography of William Hartnell by his granddaughter, which I'm sure has a good deal to say on Hartnell's involvement with the show. I also found autobiographies for Tom Baker and Elisabeth Sladen, as well as a book about Robert Holmes.

For Modern Who, The Writer's Tale by Russell T. Davies is probably the book you're looking for. I haven't read any of the above personally, but have heard very good things about RTD's book in particular.

As sort of a bonus item, Don't Panic: Douglas Adams & The Hitchhiker's Guide to the Galaxy is sort of a biography of Douglas Adams's work, from his college sketch show days to his acquaintance with Monty Python, the radio, book, and television successes (and stresses) to Hitchhiker's, and more. There's also a chapter and a couple other mentions of Adams's work on Doctor Who, placing it in the context of his larger career and the ideas he used and recycled from one franchise to another. And, to top it all off, this book is lovingly researched and written by Neil Gaiman. This is the one book out of this list that I actually have read, and if you're any sort of Douglas Adams fan, the book is wonderful.

Doctor Who: The Vault is a really good introduction to the history of the show. https://www.amazon.com/Doctor-Who-Vault-Treasures-First/dp/0062280635