The reason I suggested you just start off with discussing the class you share is because you don't really know her and I got the impression that you wanted to avoid feeling embarrassed or rejected.

Have you ever read much or watched videos about reading people's body language? If this isn't something you're skilled at, you might want to try learning more about it. It will help you in all areas of your life.

You asked what I'd prefer, though. I'd prefer safe small talk before or after class. If I wasn't at all interested in the guy, I'd let it end at small talk. I might like the guy somewhat and think of him as a friend. Or I might find him very attractive and want to get to know him better. It can take several times of talking with someone you meet in a class before anything else ever develops or sometimes you can end up immediately going to get coffee together.

I just remembered something that made me smile. When I was a freshman in college, a male friend of mine told me that he asked a girl from his math class on a date (he had never talked to her before) and she told him that she was going to be washing her hair that night. (That was like a 1950s excuse - very obviously meant she wasn't interested.) He mostly laughed about it, but his feelings were hurt a little bit. He wasn't really shy, though.

Starting off with safe conversation is considerate of the girl's feelings, too, if she's not interested in getting to know you any better. Most girls don't really enjoy hurting someone's feelings.

I hope you will make some female friends in college, too. I had a tech-y major in college and had lots of guys in my classes and ended up with nice study groups with both guys and girls in them. If you make friends with girls, then you can ask them these kinds of questions.