Shoot it, run. This is the convention that BioShock avoids with aplomb, instead delivering a unique experience.
The main enemies you'll encounter are "splicers", normal citizens who have been driven mad by modifying their genetic code too frivolously and are now monsters willing to attack on sight. You will quickly acquire a wrench and the electro bolt plasmid, giving you a handy combo to start off with. The general choice of weapons and plasmids throughout the game is excellent. You have your standard shotgun and machine gun, but also a crossbow and a chemical thrower. Your choice is further expanded by the variations of ammo available. You have standard ammo for each weapon, but you can acquire two variations. For instance, the shotgun has standard shells, electrically charged ones and exploding ones. You can also upgrade your weapons by using machines which offer two upgrades for each weapon. Unfortunately you can only use these machines once, so choose wisely.
The plasmids are a fundamental part of the game and generally very fun to play with. Possibly the coolest thing you can do is levitate and throw objects, and catching an enemies bomb and hurling it right back is the most fun you've had in a long time. To acquire more plasmids, you need to collect a substance known as Adam, which can be gained from little girls who go round collecting it from corpses. Sounds easy, right? Nah ah. They're guarded by Big Daddies, which are guys in huge metal diving suits. They are very tough and take a lot of hits to bring down. You don't have to fight them, unless you attack them they'll ignore you, but you really should look to put them down. You can then either rescue the little girl or harvest her (save or kill her). If you save her, you only get half the Adam, but it has a direct effect on how the game plays out.
There are a number of other things to note, such as the ability to hack machines. You need to arrange a series of pipes to direct a circuit flow from one point to another to achieve this. The benefits include a reduced price on ammo and other essentials at vending machines or getting gun turrets to fight for you.
Graphically BioShock looks incredible. It's maybe not as technically accomplished as Gears of War (still the standard to match visually), but it has a certain style which can make you stop and stare in a similar fashion. No multiplayer either offline or online, but BioShock doesn't have the deep combat or physics to accomodate it in my opinion. What 2K Boston/ Australia have instead done is create a stellar offline single player experience that keeps you coming back for more. It just goes to show that it can still be done.
Do you remember the time a few years ago in the PS One era when games couldn't rely on graphics or physics to guarantee sales? Instead developers had to create something new and exciting to tempt people. And this is the stake through the heart of conventional shooters driven in with devastating aplomb by BioShock. It's new, it's exciting, and it's waiting for you.
"Is a man not entitled to the sweat of his brow"? - Andrew Ryan, creator of Rapture.