Finding a camera with a very short shutter lag is the first problem.

Casio and Kodak has done the best job of reducing shutter lag for cameras in the $300 range. But they also have weak video mode specifications for most of their $300 cameras.

The $300 Sony cameras have short shutter lag and good movie specifications but people report some fuzzy photos in low light situations if you do not hold the camera perfectly still.

The other major camera companies have average shutter lag and mostly good movie mode specifications.

If movie mode is not that important to you, check out the Kodak Z730. It is a newer version of the Kodak CX7440, which got much praise.

If you do not do much low light or flash photography, check out any of the $300 Sony cameras.