The reading order for the 'Bruno, Chief of Police' series is pretty straightforward if you're just going for the main novels. Honestly, just stick to the publication order. Martin Walker has a habit of casually mentioning past case outcomes in later books, and you'll spoil minor resolutions for yourself if you jump around. Publication order is: 'Bruno, Chief of Police', 'The Dark Vineyard', 'Black Diamond', 'The Crowded Grave', 'The Devil's Cave', 'The Resistance Man', 'The Children Return', 'The Dying Season', 'Fatal Pursuit', 'The Templars' Last Secret', 'A Taste for Vengeance', 'The Body in the Castle Well', and 'The Shooting at Chateau Rock'. There's also a more recent one, 'To Kill a Troubadour'. I tried reading 'The Resistance Man' first by accident once because it was the only one my library had, and I spent the first two chapters utterly confused about who this Bruno guy was and why everyone kept referencing a case involving truffles.
If you want the absolute complete experience, there are a couple of short stories tucked away in anthologies or online. 'A Market Tale' is a nice little prequel that gives you a sense of Bruno's life before the first book, but it's not essential. The charm of the series really builds over time as the village of St. Denis and its characters become more familiar. The order matters less for the mysteries themselves, which are mostly self-contained, and more for the character arcs and the evolving relationships. Seeing Bruno's friendships with the Baron and the Mayor develop, or his various romantic entanglements, has a much better payoff when you've followed them from the start. The later books also deal with more serialized elements, like the ongoing archaeology subplot, which would just seem random out of context.
Honestly, the biggest reason to follow publication order is the food and wine descriptions. Walker introduces local delicacies and vineyards gradually, and reading them in sequence feels like a leisurely, multi-course meal through the Périgord region. Jumping into a later book where he's casually describing a specific vintage from a vineyard he spent a whole earlier book exploring just doesn't hit the same. You miss the foundational delight of it all.