In a way, I'm the perfect audience for this: biblical stories are not second nature to me (I did not remember that David came after Moses, for example), but I know enough of the broad outline of the Torah/Bible that I'm not completely in the dark. In other words, I understood David's overall importance but I'm not attached to a specific vision of him or the people who inhabit his story.
The book is told from the point of view of Natan (Nathan), his seer and one of his counselors. Having seen David murder his father, Natan is all too aware of David's frailties. But whether he can hear the prophecies emanating from him or not, Natan also *knows* that David will be the man to unify and transform their people from a group of tribes constantly in danger of being plundered to a strong nation that is feared and later respected by its neighbors.
The tension that drives the story of David is that he must do "whatever is necessary", however ruthless, in order to serve the Name. And there is much that Natan knows the Name can allow, whether it's his passionate affair with Yonatan, son of Shaul (and brother of his first wife Mikhal), his indiscriminate murder of all villagers who stand against him, or his general intemperance and lust. All of that is balanced against the way in which he can measure a man (or woman) and, as Natan says, meet them where they are instead of demanding that they meet him on his terms. But unlike his treacherous son Abshalom, he doesn't make a show of it as a glad-handing politician; he genuinely wants to be genuinely loved and respected.
What the Name- and Natan- finally cannot overlook is the crime he commits against both Uriah and his wife Batsheva when he rapes her and then causes Uriah to be killed so that his sin won't be discovered. When Natan famously tricks him into cursing himself, David does public penance, but he's finally gone too far to be forgiven without paying the four-fold price he himself decreed was due. Unfortunately, the price was four of his children: Batsheva's first born, his lecherous, incestuous son Amnon, his only daughter Tamar, Amnon's victim and Tamar's full-brother, the vengeful, ambitious Abshalom. His saving grace, and why Natan stays with David: Shlomo (Solomon), his eldest son with Batsheva, whom both she and Natan foresee as having the vision to eventually lead the nation David established, who can finally transform "whatever is necessary" into "what is just".