If you liked the show, and i can't imagine what kind of slack jawed faggot wouldn't, definitely read the book it goes into a lot more inner personal monologues of major characters especially Toranaga and has a bit more about the western european politics of the period.
It also has a fuck ton of stuff about anal beads, pillowing, and farting which I did not expect. its a pretty massive book although the editions with Tom Hardly on the cover are split into 2 books, Shogun I and Shogun II. There are like 6 more books by the author covering asia as well but none in the same time period.
I haven't read them yet but other recommendations I've seen on reddit are Taiko about the Taiko's rise to power (Toranagas boss), Confessions of a Yakuza (similar rags to riches and power plays), Samurai Warrior (about another white guy who became a samurai), Samurai Warfare about japanese warfare during multiple shogun periods, Shogun: The Life and Times of Tokugawa which is a biography of Toranaga
i hope the success of Shogun spawns a bunch of historical well done dramas about other empires like ancient China, Mughals, Egypt, or even something like the Mayans or Aztec could be very interesting. or for the lulz We Wuz Kangz