Asking a classmate out?

So there is this girl in my class in medical school, this will be my class for the rest of the coming years with the exact same people, and I have been there for over a year now, so even though it’s a big class (about a 100 students) everyone knows everyone, at least to a certain extent, and everyone has everyone on their facebook. The extent of my relationship with her is just the every day smile and “hi”, and some minor facebook interactions, we also have many friends in common, but these are neither my best friends nor hers. I don’t know if she’s seeing anyone but it doesn’t look like it. She is extremely friendly, so it’s not difficult to strike up a conversation with her, and I believe I have already left a pretty good impression.
Ok now the reason that scares me of doing something about this seemingly simple situation is that we are going to be in the same class with the same people for years, and I don’t know if I can deal with a rejection in such a situation, I also fear the downfall of having such a relationship in first place.
My plan of action is to take our everyday relationship to a higher level, and then maybe sometime ask her out casually, either with some mutual friends or to some other place where I usually meet some of my non medical school friends, and from there I’ll see what to do. I just don’t want to end up in the friends zone, or embarrass myself.
I want your input on the subject. Thanks in advance and sorry for the long text.