That's normal for it to be in Common since it's not a Valve product. Only Valve products, like TF2 or CSS, show up in your username folder.
Can you tell us the specifications of your computer, including operating system? Would help if we knew what your CPU/Video card/Amount of RAM/OS is.
If you don't know how to check, a combination of browsing the Device manager and Computer Properties will help a lot.
Computer Properties will tell you name of CPU and amount of RAM, as well as OS. Device Manager will tell you pretty much everything else you need to know. Display adapters is where you need to look under the Device manager to find your graphics card.
If we know your OS, we can find a specific fix for that operating system + game. We can also tell if your computer is capable of handling the game. If it doesn't meet the requirements, you cannot play the game.
You can usually tell if your computer can run the game with
http://www.canyourunit.com/ - however, it's not always accurate.
Here's a quick fix I found that may work, too:
Find your BioShock shortcut, right click it, click properties, and add "-dx9" to the URL.
It should look like this:
Code:
"steam://rungameid/7670" -dx9