Uhura’s Song was a lovely book, as I recall (it’s been 20+ years since I read it). I don’t know that there are any “must read” original series books, though. I did enjoy the TNG novel where Diane Duane crafted a mirror universe version (long before DS9 revisited the mirror universe). And as a teenage fan I enjoyed Diane Carey’s Dreadnought, even though it is Mary Sue fanfic of the most obvious kind. But her later Trek novel, Final Frontier, is quite a good one. I have a signed paperback.
Actually, I did think of one “must read” TOS novel: Yesterday’s Son by A.C. Crispin. Her first professional sale, and it’s still a good read. It’s a sequel to “All Our Yesterdays,” so between that and the novel’s title, you can probably figure out the basic plot, but it is a really good book. She nails the characters’ voices and motives.
Shameless plug alert: I have a story in the second Strange New Worlds anthology, published way back in 1999 – it’s out of print now (alas!) but you can maybe pick it up at your local used bookstore or through Abebooks or Amazon Marketplace. There’s also a lot of other great stories in all the SNW volumes – the tenth and final one was published last year.