What I want to do is create a “category page” for each category
That would be category archive, not page. See category templates.
As all of my “product detail pages” are pages, and not posts, I’m not sure how to set up my taxonomies.
It would make sense to create custom post type for your products, rather than trying to repurpose pages.
The other issue is that I’ve found plenty of information on how to use taxonomies to display, for example, a list of posts that correspond to a given taxonomy. But what if I simply want to display those three things for each product that corresponds to a given taxonomy?
You can customize template to display whatever you want. Loop will go through posts in category, but you can use any (or none or whatever) template tags to display information.