What’s the most important factor to get clear images using high telezoom on moving subject?

So let’s assume I’ve got the focus nailed down, so my focus is the best possible. I have a single subject I’m shooting at very high telezoom on Panasonic TZ-80, using 60x or 120x zoom, so the camera is quite shaky.

From my basic research the following options could be possible to get the clearest image:

  1. Force aperture to the lowest possible value to give highest depth
    of field in case focus is not so accurate (i.e. subject is moving so camera makes mistake or can’t keep up)
  2. Force shutter speed to a very high value
  3. Force ISO to a low value

Since these all work against exposure, I can’t do everything. Is there one of these in particular that are likely to be my best option or would I have to experiment?