Comparing mini pumps - what to look for and what to consider?
You need a pump that pumps air, to the pressure you ride at, through the valve system you have.  And you need that pump on you or your bike, not at home.

Lighter weight is nice, but super light tends to be weak and bendy.  

Some pumps allow the use of CO2 which sounds nice, but gets expensive.  Plus that tyre will be low/flat the next morning. So carry a pump as standard and a co2 inflater as optional.

I have 4 bikes.  At a minimum, each has its own pump, tool kit (multi tool, 2/3 tyre levers) one spare tube, and stickers.   That way I don't get stuck somewhere without the bare essentials.   Consider this, should finances stretch that far.

Mini pumps generally come with a clamp that fits under the bottle cage mounts, or some have more unusual mounts.  There's a risk the pump gets stolen if you leave it there, or may vibrate loose and fall off while riding.  A velcro strap helps, or a ziptie that you cut off in time of need.