The reason I said rent it first because it is different that your average FPS. The levels are not linear and you may spend a lot of time looking for things. But the developers thought ahead and will give you hints.
Basically, the character Jack finds himself crash-landed in the middle of the pacific ocean. He runs to a nearby lighthouse to seek shelter. Where he finds himself a few minutes later, plunging into the water in some sort of submarine to see a city built underwater. Jack listens to the "Tour guide" saying that the city is awsome blah blah blah. But it turns out it's corrupt due to.....well......"Drug" addicts.
The drug is actually a mutagen that allows the taker to plasmids which are basically super powers. Your main enemies are Splicers which are ADAM addicts and abusers.
Now about the gameplay: The levels are very dark and confined. This makes it intially hard to navigate throughout. I one time missed a weapon and that made it really hard. But eventually you'll get used to it and the game will be fun and a breeze.
Your weapons have different types of ammo like armor-piercing, anti-personell which I think is very original. To get ammo and other items, you can buy them from cheesy 1950 vending machines or search desks, cash registers and bodies.
You starts off with the electro-bolt plasmid. This gives you the ability to stun oponents with an electric shock. At first you can only have two plasmids at a time, but you can buy more at ADAM vending machines.
How do you get ADAM? From these little girls who run around, extracting ADAM from dead bodies for recycling. The catch? They are protected by these really tall, armored guys called Big Daddies. Don't let the name fool you, these guys are tough; especially the first few. But like everything else in the game, IT ALL gets easier no matter how frustrating it may seem.
In conclusion, Bioshock is an awsome game. If you don't feel like buying it, I urge you to try it.