For action shooting, the Z3 will be the best of the bunch.
Here are the timings for the cameras you mentioned.
The first number is the time (in seconds) to capture the photo if you pre-focus by holding the shutter button half way down to achieve focus lock.
The second number is the time (in seconds) to capture the photo if you do not pre-focus.
Z3 - .1 - .2
Z2 - .1 - .4
S5100 - .1 - .6
770 - .2 - .8
Most of these cameras also have a "burst" mode that let you take photos in fast succession. This is a very handy feature.
At the moment I am looking at the Konica Minolta Z2. However, I would give serious consideration to cameras like the Minolta Z3, the Olympus C-770, or the fuji S5100 if anyone would recomend them. I am mainly looking for a high zoom camera with decent resolution (3-4 megapixels, preferably 4) and a fast shutter reaction, if only to avoid missing shots. I mainly photograph wildlife and have found that static pictures are not nearly as exciting or impressive as action shots.