I'm trying to recall the questions I had at the start...
1. How much money?
I couldn't have started when I was student; it's not crazy expensive, but it's not free. A kayak can cost anywhere from a few hundred (these are Canadian Tire, really just big water toys for cottages) to thousands.
I spent 1200 (tax in) for mine, a Venture Flex. I picked it partly because it's shorter than most; that turns out to have some downsides (only one bulkhead, which makes bailing and self-rescue impossible, which demands I keep within swimming distance of the shore) but is mostly great. This is important if you live downtown - my backyard and storage space are limited. It's a wide kayak, which is a nice thing if you're just exercising and taking photos and meditating, which is what I'm up to; the thinner ones are faster.
Prior to that I bought a used inflatable kayak (not as silly as you'd think, not as useful as you'd wish) from Advanced Elements. I got it for about 400 on kijiji, and will sell it sometime soon - go used. More on ups and downs of that choice later, probably. Long and short: slow, stable, nice, recreational (not good for exercise, says I).
You'll need some gear, too: a way to transport it (foam blocks and ties do the trick for me); a lifejacket (kayak life jackets are shorter than canoe - ask in the store. I bought the wrong one first, cuz it was on sale, and had to replace it). A paddle, obviously; a safety kit (a rope, a bailer, a whistle and a light (legal requirement and good idea).