Well there a couple of main decisions the OP will need to make concerning the framerate and the shutter speed, and these will depend on the type of look/feel he's going for. The first is the framerate - 24fps is regarded as giving a Hollywood film look, 30fps is used for most television broadcasts, and 60fps can be useful if you want to slow the footage down to 24fps or 30fps for dramatic effect.
Then there's the shutter speed. Usually it's based on doubling the framerate, so if you shoot 24fps then you need a 1/48 shutter speed, 30fps needs 1/60th shutter speed, and so on. This creates a certain amount of motion blur which we, as viewers, have become used to. But it's not uncommon to see much faster shutter speeds being used in videos nowadays - BBC's Top Gear often use Go Pro cameras in their footage and they usually have a much faster shutter speed resulting in less motion blur and a slightly choppier looking video as a result.
The action sequences in Saving Private Ryan (and also the island scenes in the TV show Arrow) are also shot with a much faster shutter speed, which conveys a feeling of frantic action. They could have shot the footage with a shutter speed of 1/48, but the resulting effect would be quite different.