Having been down this particular rabbithole recently there are lots of things to consider, but as concisely / efficiently as possible:
Ascertain what tyre pressure you need to achieve with this calculator.
Use that to sort through appropriate pumps; IME quoted maximum pressures are "optimistic" by a factor of two - i.e. if a pump says it'll do 120psi, it's reasonable to consider that it'll do 60psi without becoming decidely unpleasant.
Not the for a given pump size / form factor, you'll get two extremes and a load in between, ranging from high-volume-low-pressure for stuff like MTB tyres to low-volume-high-pressure for road bike tyres. Choose wisely as going-un-necessarily high on the pressure will mean an excessive number of strokes of the pump to fill the tyre.. while going to low on the pressure will mean you'll not be able to attain the pressure you need.
Note that the max pressure achieved by a pump is a function of its internal geometry, not size. Displacement of the pump is dependent on both geometry and size, so all things being equal a larger pump will displace more and require fewer strokes to fill the tyre.
Some view the portable pump as a "get you home" solution that doesn't need to fill the tyre quite to the necessary pressure - just enough to get back without wrecking the tyre. While there's some merit to this, I prefer something that's capable of properly filling the tyre if possible, although this limits your options a bit as there will be fewer properly suitable offerings.
Seems the tyres on your bike are of a reasonable size (maybe 32-38mm wide..?) so hopefully you shouldn't have to go too high on pressure, which will give you more options.. unlike when I was shopping for a pump for my Brompton, which likes 100psi in the back. Settled on a Topeak Road Morph (they do other lower pressure, higher volume offerings too) which has so far acquitted itself well
