A lot of this depends on how frequently you're looking at carrying stuff. As others have mentioned, things like locks and flat kits are generally easily located on the bike itself/ in a smaller, bike mounted bag. Books, laptops, clothing, and other larger, heavier, bulkier items require more thought, but it isn't a 'one size fits all' world. There's lots of great advice above, but I thought I'd give you another different perspective. I like backpacks just fine. They're useful, easy to carry, and generally extremely stable (I can't imagine how one packs a backpack if load shifting is a major concern). I prefer them for flexibility/comfort when moving around off the bike, non-biking utility and price. You can often find a reasonable general duty backpack for under $50 (depending on your needs/ preferences, and if you're willing to accept a non-cycling specific pack) and really nice ones are still under $100. A cheap rack will set you back $20 (and they can potentially cost way more) and decent panniers will usually cost more than that.

I think panniers are great as long as you don't expect to be doing much moving off the bike, such as walking to and from classes within enormous university or within large office buildings, for example, unless they have decent carrying straps or backpack straps (which usually puts you into the higher price points, in my experience). I cycled with a backpack until just recently, and it wasn't til I started riding more than 10 miles each way that I really felt the desire/need to switch over. The down side to non-cycling backpacks is that they don't always place the load where you want it for cycling, esp. if you're riding in the drops. But this is a highly personal choice/tolerance issue. Some people complain a lot about sweaty backs. I sweat no matter what, and the backpack just collects the sweat in a different place. Another thing to remember: a rack and panniers will add weight on the bike, and the rack, at least, is not so easy to remove for fun rides. It also means the bike is heavier if you have to carry it up stairs, or lift it onto a storage rack.

I've never tried a messenger bag, but if you go that route, be sure to get a real one, not a messenger look alike -- it needs to be properly stabilized for riding. My one experience was trying to use a briefcase with a shoulder strap, and that was near disastrous. I think a good messenger bag would be ideal for the riding/carrying you've described, however.

Whatever you choose, be ready to consider alternatives as circumstances change or your preference become refined. Keep riding!