The most underrated starting point is actually her Bardic Voices series, book one 'The Lark and the Wren'. It's a zero-to-hero story about a stubborn street musician who literally charms monsters with her music. The magic is all music-based, which is unique and beautifully described.
It's also set in a world with a rigid class system, so there's great social conflict. It's a complete story that opens up a bigger world. If the idea of magic being channeled through art and performance appeals to you more than psychic bonds or elemental spells, run, don't walk, to this book. It's a masterpiece of a different color.
Anyone else get emotionally attached to the Companions more than the Heralds sometimes? Rolan, Gwena, Yfandes... they're characters in their own right. The order you read affects which Companion you meet first and who becomes your favorite. That's a weird little side effect of reading order no one talks about.
Oh, the publication order is definitely the way to go. I tried jumping in mid-series once and was completely lost with all the recurring characters and personal history. 'The Silver Pigs' is your bedrock. After that, it's a pretty straightforward run: 'Shadows in Bronze', 'Venus in Copper', 'The Iron Hand of Mars', 'Poseidon's Gold', 'Time to Depart', 'A Dying Light in Corduba'... the list goes on to about twenty books. Wikipedia or Davis's own website has a complete numbered list that's easy to follow.
Her adult psychological thrillers are the main draw for most. I'd recommend starting with 'All the Missing Girls' because it put her on the map, then just follow your mood. Each book has a similar tense vibe but a unique setting.
My friend got into them by reading 'Owlflight' first, which is the start of the Owl trilogy, set in a different part of the world. She loved it and then branched into Valdemar proper. There's no gate here.
The practical method: Wikipedia. Search "Marcus Didius Falco." The page has a list of the novels in the series, clearly numbered in publication order. Print that page or save it as a PDF. Problem solved. It's the most authoritative free source. Then, all you need to do is find the books, which is getting easier with ebooks and reprints.