An interesting selection.
All three are about the same size and weight.
Just enough differences between the cameras to give you some choices.
If you are wanting to get more involved with photography, the P300 gives you the advantage of having the important manual controls (shutter priority, aperture priority, full manual).
The other two cameras do not offer these manual controls.
If you need a camera with a lot of zoom, then look at the S9100.
The S8200 has 16 megapixels, which I would avoid.
That is too many megapixels on such a small sensor assembly.
Generally a 16 megapixel sensor tends to be noisy.
That results in needing to use noise reduction firmware in the camera and that reduces detail.
The other two camera use 12 megapixels sensors which should give you acceptable ISO up to (and including 400).
I have narrowed down my options to: