[Detecting Thrown Ball] Which camera to use and which arduino board to use?

Anchun:
For my current plan, what the Arduino does is,

-receives an image without the ball in presence, and store it as "background" image

I think you will find this is more or less a complete non-starter. People have got low resolution black and white images off cameras, and some clever people have got an compressed colour image off a camera, but the Arduino doesn't have sufficient resources to decompress the image let alone do anything with it. You really need a computer to tackle this problem, not a microcontroller. If you add a PC to your solution, it would be possible to put together a solution very easily - in fact there is freeware software available that already does this sort of thing.