So this is an example of why you should always start by sharing information about the hardware you have. Had mfenn not asked you about it, you'd have just wasted over $100.
Forget the power supply - that's a slim desktop, and will not fit anything but a low-profile, single-slot graphics card in it. Basically, you're not going to do a lot of gaming on it.
This HD6570 is the most powerful card you can fit in your system, at $40AR: http://www.newegg.com/Product/Produc...82E16814102994
It will give you a nice boost from the Intel HD4000, but certainly won't allow you to play modern games at anything other than low settings. I doubt you'll actually be able to play Battlefield 3 on it satisfactorily.
Will I be able to Play BioShock Infinite and AC3 without lag?