How you choose to dress on the first day is determined largely by how you wish to present yourself to your students. You can present authority, be relaxed, or find a median point between the two. For the first day, many experienced TAs recommend dressing professionally. Your students will be expecting this, and through years of conditioning will naturally defer to your authority and presumed expertise so as long as you perform the role of instructor in accordance with their expectations. However, other TAs feel uncomfortable in professional dress and are happy teaching in jeans from day one.
Younger TAs who are concerned about establishing authority in the classroom have stated they find dressing professionally is an easy way to help differentiate themselves from their students in manner of dress since there won't be much difference in age.
Professional Dress Recommendations
Men: Pants or slacks, long sleeve shirt, tie, sport coat, dress or dress casual shoes
Women: Pants and blouse, dress, skirt (with length), flats or sensible heels
If you choose not to wear professional attire your first day, we at least recommend not dressing too formally or informally. Just imagine how your students might react if you came to class dressed like this:
Many TAs prefer to dress professionally the first day or first week, and then relax their dress over the course of the semester. To see what TAs are teaching in as the semester progresses, check out What to (and not to) Wear.