How do you buy an engagement ring?

Hi all. I am buying my girlfriend an engagement ring soon, and I need help!

All I remember is what I learned about the 4 C’s in a college speaking engagement: color/cut/clarity/carat.

What is the most important to you (girls especially please sound out)?

I know about shape, and carat. So I’m more curious about the other sections. Can you recommend a site I can use to look up the grading scale for this stuff?

Real prices? Also, if I haven’t asked any critical questions, please feel free to add those as well (with answers!!!)

Thank You :)