Oh, this is actually a simple one. The books for the main series are numbered right on the covers, so that's your easiest guide. It's 'Dog Man', 'Dog Man: Unleashed', 'Dog Man: A Tale of Two Kitties', then 'Dog Man and Cat Kid', 'Dog Man: Lord of the Fleas', 'Dog Man: Brawl of the Wild', 'Dog Man: For Whom the Ball Rolls', 'Dog Man: Fetch-22', and 'Dog Man: Grime and Punishment'.
Stick to that order for the overall character and villain arcs, like the progression with Petey the cat. The more recent ones kind of assume you've seen his earlier changes. Also, there are some companion books like the 'Dog Man: The Supa Buddies Collection' or 'The Cat Kid Comic Club' series, which are fun but exist sort of alongside it. You won't be lost if you read the numbered ones in order, and that's the core of the whole thing.