Get something of the appropriate size for you from a place like Blacks or Mountain warehouse, the sort of thing that could be used by someone hiking over distance. Not stylish whatsoever but for people who are commuting and who have to wait for buses or walk to and from their car it's the only way. A pack that will swallow a full blown lever arch file, a sizeable text book. your laptop, your lunchbox/bag, your coat, a water bottle, flask and all the other essentials needed for a day at University is the only way. Tote bags, satchels and smart leather shoulder bags though more stylish, just won't be as comfortable to carry and they won't stick being rained on.
Buy a rucksack, mine is a 40+10L one that I have had for years. 40+10 is pretty big, possibly borderline too big but I lived with it daily at Uni. You can buy a drawstring rain cover for not a lot of money if yours doesn't come with one, no worries if you get caught in a rainstorm waiting for the bus that way as you can just pop the cover on it.
The sort of thing you see people go to secondary school with might just about suffice but they just wouldn't have been large enough for me. I'd say 20 litres might work as a minimum but that is my own view and others might disagree.
I have a lovely and well used leather satchel/shoulder bag from my previous life but didn't ever have to walk very far with it on my person. It's just about large enough for a professional who is office based to use but it wouldn't hold much more than an A4 lever box file to be honest.