Will Fallout 3 work well on my PC now?

Depends. If you had all the recommended system requirements for Fallout 3 before you made this purchase, then the 9600 GT will dramatically increase your PC's performance. The NVIDIA Geforce 9600 GT is a fairly modern graphics card currently available on the market. It will play Fallout 3 easily on full settings (the game only requires a pathetic 6800 accelerator card). However, having said this, the 9600 GT will make little difference if your total physical memory or RAM is only 1 GB or under, as you may still have issues of lag or other complications with Fallout 3. For gaming at the moment you should at least have an AMD 4500+ running at 2.0GHz. On top of that, you MUST have a dual core processor or above.

Windows Vista/ Windows XP CPU: 2.4 Ghz Intel Pentium 4 or equivalent processor Windows XP: 1GB System RAM / Windows Vista: 2GB System RAM Video Card: DirectX 9.0c compliant video card with 256MB RAM (NVIDIA 6800 or better / ATI X850 or better) ABOVE ARE THE MINIMUM REQUIREMENTS FOR THE GAME IF U HAVE ENOUGH RAM U MIGHT BE ABLE TO RUN THE GAME AT DECENT SETTINGS.

Well that kinda depends on what you had before, doesn't it? Fallout 3 is fairly well coded so you should be ok graphics-wise, but it also depends on what else you got in the PC.