Alright, let's get into this because it's a classic case of the show totally overshadowing the source material, and the order gets messy fast.
The books are actually a series of novellas by Luke Jennings, originally published as e-books. The first three—'Codename Villanelle', 'Villanelle: Hollow Point', and 'Villanelle: Shanghai'—were later compiled into the print volume 'Killing Eve: Codename Villanelle'. That's your starting point. Then there's a proper sequel novel, 'Killing Eve: No Tomorrow'. So in simple order, you've got the compilation first, then the sequel.
But here's the wrinkle that makes people scratch their heads: the books are a different beast. They're grittier, colder, and Villanelle is even more of a terrifying void of a person—less darkly charming, more outright psychopath. The dynamic with Eve is there, but it's not the slow-burn romantic cat-and-mouse the show perfected. Reading them feels like getting the blueprints for a sculpture that someone else then made iconic. There are no prequels beyond that initial origin story in 'Codename Villanelle'. I'd say go for the compilation, see if you vibe with the prose, and then decide if you want the closure of 'No Tomorrow'. The ending there is... abrupt, and honestly left me a bit cold, which might be the point, but it's not the satisfying narrative arc most TV fans are hunting for.