Why not both?
I know it’s kind of a faux pas to use your handbag for school stuff, but I’m a woman of streamlining and I can’t be bothered to carry separate bags. Get a decent tote or messenger style purse with lots of zippers and pockets. Make sure it’s big enough for a laptop/tablet, and that the straps can comfortably support the weight. Then just get down to essentials. A notebook, pen, pencil, charger, wallet, phone, keys, ID, compact, lipbalm, DONE.
Nothing says first year like a Jansport, so please for the love of God and fashion, don’t do it.