A quick note on pannier racks: I switched from a rucksack to panniers in my second undergrad year, and I must admit that it wasn't incredibly useful at first. Carrying a few books and lecture notes, a rucksack is only inconvenient on the bike if you're cycling more than a few miles. But then when you arrive and get off, you're probably spending a few hours carting that bag around lecture halls and libraries, which is much easier with a rucksack than a pannier bag.
In short, there's a trade-off. While you're on the bike, if you've heavy cargo (such as groceries) or a long distance to travel, it's much easier to make the bike carry the load in panniers. But when you get off, if you're walking around, a rucksack is easier to carry. Some pannier bags have shoulder straps to make that easier, but I find with my Ortlieb Back Rollers the straps are too much faff. You can also find pannier bags that transform into rucksacks, but I've no experience with those.
Having a rack on the bike means that even if you think a rucksack is the best option, you can change your mind later, or have both and use them at different times (e.g. panniers for shopping, rucksack for lectures).
A last quick note: if you can't afford to invest in a fully waterproof rucksack or panniers (they're a good investment when you can!), keep a plastic bin bag in them to stop your books getting wet in the rain. Also, you might want to stuff a plastic bag under your saddle, so it's handy to keep that dry when it rains. You don't want a damp bum distracting you in lectures, or inviting speculation on your nights out.