Please do NOT show up with a briefcase. Take a backpack or whatever you're comfortable with or normally use for books. Dress just like you did in undergrad.
Find out if your law school allows computers in class (most do). If not, you'll obviously need stuff for taking notes. Also, highlighters and pens and junk. Really, law school is just like undergrad in so many ways. Whatever method worked for you there will likely be pretty effective. It got you this far!