I find the publication order more comforting. You meet the most beloved characters first. Royce and Hadrian are your gateway into this world. When you later read about the ancient heroes they occasionally mention, it feels like uncovering treasured family history. Starting with the ancient history feels more distant, less personal.
What's the rush to know the whole timeline? Savor it. Read 'Revelations' and fall in love with the world. Then, when you crave more, you have two whole other series to dive into that expand the history in thrilling ways. Knowing the entire chronology upfront is like reading a spoiler wiki before watching a show. Half the fun is the discovery.
The purest, most enjoyable experience is the publication order of the core Riyria books: 'The Riyria Revelations' ('Theft of Swords', etc.) first, THEN go back and read 'The Riyria Chronicles'. Those chronicle books are like delicious dessert—extra adventures with characters you already love. Reading them first would be like eating your cake before the main course; it's still sweet, but the meal's structure is off. Save the prequel treats for after you're fully invested in the duo.