If you have any interest at all in fairy tales, folk tales, and mythology, you should read Andrew Lang's Colored Fairy Books. The books are littered with cautionary tales of heroic men and women who overcome symbolic and literal challenges that are both ancient and modern. And if you hate "princess culture," they may help you and your child expand your definition of the label "princess." At the very least, they would give you reason to start a conversation with your child about gender roles and culture throughout history.
Although their contents of traditional folklore was bowdlerized for the consumption of an audience of prudish adults and young children, they maintain the diverse cultural references you'd expect of oral stories collected from around the world. Many of the stories are vastly different from one another. But even more interestingly, many of them are surprisingly similar. If you read all of them, you might see Joseph Campbell's monomyth theory in action.