Look for an nVidia 9500GT since it does not draw a lot of power and will do a decent job on your computer for games. the ATI 9200 is an AGP card and your motherboard uses a PCIe slot so that's why it won't fit.

If you get anything higher than the 9500GT you will (probably) need to replace the power supply on your computer as well, since most computers sold retail - like Wal-Mart of Staples - typically have a very basic power supply installed.

Here are some for you to choose from should run be fine for you - at medium settings, maybe high with no AA and no shadows: Click Here

supposing your computer is less than 3 years old it very likely has a pci-e x16 slot (this is the reason why your old 9200SE graphics card doesn't fit because it has an AGP interface).

the presence of the GeForce 6150SE tells me that this PC very likely has a weak 250W psu, so you haven't many options for the upgrade of the graphics without an upgrade of the psu at the same time.

the best low power graphics card that will run with the existing psu is the ATI HD 4650 (it's faster than a GeForce 9600GT). this graphics card surpasses the requirements for Bioshock by far and doesn't cost a fortune.
Click Here

nVidia 9800gt, this will fit in the PCI slot, and I think it is under a hundred dollars, but you should check to see if it fits in the actual computer case.