If you are looking for a game to get with your new 360, this is the one.
Your in a plane, it crashes in the middle of the ocean, and you discover an underwater city called Rapture. The story line unfolds as you keep playing and it actually makes you want to play some more. The main point of Bioshock is its story, which slowly unfolds as you keep playing.
What's great about Bioshock is that you are constantly building up your charcter. You need to buy new spaces to hold plasmids (more on that later) , certain strength upgrades, certain gaming hacks, etc.. You don't just go around shooting things, you learn new plasmid spells and upgrade your weapons as you go along. This is something most FPS lack, but in Bioshock, it makes you keep playing.
The plasmids are the most interesting part of the game. You can shock and enemy with electricity, shoot a swarm of bees at them, shoot ice or fire, or even pick up a corpse and use it as a shield. And these plasmids are all upgradeable as well. It's fun to test out different plasmids because they are all useful in their own special way, although the electric plasmid is the most useful one.
If you are using a weapon, the combat really isn't that great. But the combat isn't the main focus of Bioshock, I mean its still fun, but its not the main focus of the game. Plasmids make do the combat tons more interesting, however.
Another great thing about Bioshock is you have the ability to make certain weapons attack your enemy, besides you. For example, when you first encounter a security camera it triggers an alarm and these little security helicopters start firing at you, well you can hack that security camera and if the camera sees an enemy, the security helicopters will go after the enemy besides you. And you can do this for a number of different machine weapons you will encounter in the game. You can even hypnotize a Big Daddy (which are the big machines that you must kill throughout the game) to protect you.
Overall, Bioshock is a great game. It's not your typical FPS, so if you're looking for just a shoot 'em up game where you just shoot things all day, this isn't for you. There are better things then just combat in this game. If you just got a new 360, this is the game to get with it.