So, like any good 21st century learner I immediately went online to learn how to purchase oranges. According to Pittman & Davis (Tree-Ripened Fruit and Gifts since 1926), you want to choose a navel orange that feels heavy in your hand, smells fresh and orange-y, and has a peel that is a uniform orange color. Nothing about the thickness of the peel. But it turns out that navel oranges are supposed to have a thick peel, while the Valencia orange, used more for juicing than eating, has a thinner peel. I'm not sure if choosing navel oranges with a thick peel means that I have chosen one more representative of the navel orange breed (sort of like a Kennel Club dog show for oranges) and therefore a better tasting one, or if it is entirely accidental that I continue to have success with choosing only thick-peeled oranges (which seems mathematically unlikely).
If anyone knows for sure, please let me know. I continue to choose the thick-skinned kind; they are more resilient, anyway.