Here's an attempt at a Klingon reading list, with the entries in bold being the ones focused fully on Klingons, and so probably the most important:
Enterprise: Kobayashi Maru (the Klingons' political dealings with the Coalition and the Romulans)
Errand of Vengeance Trilogy (Buildup to war between Klingons and UFP in Kirk's time)
Errand of Fury Trilogy (Continues the buildup and ends with a story that's partly a novelization of "Errand of Mercy")
Vanguard series (The Klingons compete with the UFP and Tholians to control the Taurus Reach region and its powerful alien technologies)
Seven Deadly Sins: The Unhappy Ones (ridge-heads Vs smooth-heads. The Three Ks show up)
Mere Anarchy series, books 2, 5 and 6 in particular (the Klingons meddle in the reconstruction of damaged planet Mestiko. The Three Ks show up.)
In the Name of Honor (Koloth and Kirk go on a mission to free Federation POWs)
Forged In Fire (The Albino attacks the Empire, Sulu and the Three Ks go after him)
The Last Roundup, possibly (Azetbur has her people follow Kirk and provide assistance)
Serpents Among the Ruins (Azetbur's death, political shakeup, though main focus is on UFP and Romulans)
The Art of the Impossible (Klingons vs Cardassians, the fate of General Worf)
The Left Hand of Destiny, books one and two (Martok is King Arthur)
Diplomatic Implausibility (Worf's first mission as ambassador, the Gorkon's first outing)
The Brave and the Bold, book two (Klag and the Gorkon team up with some of our Federation heroes)
IKS Gorkon/Klingon Empire series (Obviously)
Voyager: Full Circle (Klingon prophecy and the bat'leth-wielding fun this entails)
A Time to Kill and A Time to Heal (Klingons clash with UFP over Tezwa)
A Time for War/A Time for Peace (Internal Klingon politics makes Worf miserable)
A Singular Destiny, possibly (The Kinshaya take advantage of post-Destiny chaos to attack the Klingons)