A backpack is a good idea - especially if you cycle/catch public transport. Its easy to do up quickly, you can keep essentials like keys/money in the front pocket, its often got a water bottle 'bit', and its strong/hard-wearing. And its big enough to dump a pile of books and/or a laptop in and still feel comfortable on your shoulder.
Make sure you also get one that is waterproof! Avoid flimsy cotton or canvas ones for this reason - they might be nice as a holiday bag but are useless as a student bag in mid-winter. Everything will get wet and it'll fall apart by mid-term. Sports shops and 'outdoor' shops (get over your fear of Millets please....) are better places to buy than at New Look. Yes, it might seem more expensive but its worth it.