I'm one of those people who has a few bags rotating.
I have a backpack with a laptop compartment, which I use for days when I have my laptop.
I have another backpack thats pretty roomy for days when I need a lot of textbooks/library books with me (its rare that I use this one though).
I have a messenger bag for days when I just need notebooks or readers, lunch etc.
I have a big handbag for days when I don't need much at all (so maybe just exercise books, water bottle, snacks etc).
Some days when I cbf taking shit out of my normal handbag I take that and then chuck my books into a cotton on/supre type bag. Actually works better than it sounds.
Downsides to this: I am forever moving stuff from one bag to another. Its also pretty common for me to get to uni and realise that I don't have any pens/highlighters etc and have to run to the bookshop or library to buy some.
I will also point out that I think I'm a rarity. Most people I know have one bag that they use all the time, whether it be a backpack or a messenger bag, but seriously noone is going to judge you based on what kind of bag you have.