I chose a saphire because I liked blue. Not my birthstone or one of my school colors. If they don't like it, they won't wear it, so I'd let her choose what stone she wants.
For a CLASS RING, I don't see why anyone would choose anything other than the school colors. It's a symbol of your school.
If you want to choose your birthstone or your favorite color, why not go with any old ring that you like? It'll cost considerably less.