Hi! I doubt your professor will write anything negative on your referral because they will want you to do well in your career. Give them a few pointers about what you do in your spare time and topics you like studying to give them stuff to talk about when making the referral. Good Luck!
I would just dress how you normally would for an in-person job interview or as if it was your first day at a new job. I think a blazer or a blouse would be formal enough. I would also advise to wear black trousers and clean black shoes.