Hi there!
I would recommend getting a sturdy backpack, particularly if you'll be taking a laptop with you! You can search online for backpacks that have built in compartments especially for laptops, as well as plenty of back and shoulder support so you don't ache! As a former tote bag user, once I bought my backpack for uni I never went back- I have a Kanken specifically for laptops, and it's sturdy & supportive, as well as waterproof!
If you're travelling on the tube, it also helps to have a backpack with hidden or lockable zips to avoid pickpockets- totes and purses are cute, but also very easy for people to take things from, especially during rush hour when everyone's crammed in like sardines.
Unis can be quite paper-heavy, depending on your course, as well as your method of taking notes. If you have a lot of loose sheets of paper, I'd recommend getting a slim folder so that all your things are in one place.
I hope this helps!
-Ella