The parameters on the data sheet that are important for you right now are getting a low Rds(on) and a reasonably high gfS. Check there's enough Id, there should be enough, because a low Rds(on) is usually hand-in-hand with high Id. Luckily you don't have many volts to worry about. Nor is any dynamic parameters much concern to you.
Automotive 'fifth generation' FETS seem to gravitate in this direction, also TrenchFet might be the holy grail of RollsRoyce of fets for you. The curves on a datasheet are really useful, hardened engineers study them closely, and in their head these curves 'come alive' to them and they can watch them animated.
Bear in mind that paying more for a lower Rds(on) is diminishing returns, because there is still the resistance of the connecting wires, solder joints, and of course the electric motor winding resistance. 20 mΩ is sufficient, but you could get a better feelgood choosing an 8 mΩ one if it's the same price.
Rds(on) is the lowest possible resistance possible when the FET is under ideal conditions. gfS is forward transconductance, it's a fancy way of saying "how many Amps for each Volt". The two together vary the shape of the curves.
Once you've built it with FETs you believe in, and the circuit still doesn't work after that, it's still going to be difficult to tell what's really going on without recorded scope readings of the voltages and currents in the actual circuit. You'd need to set up a triggered scope and capture waveforms for studying.
PS. in a test setup, you are allowed to try things like connecting Fets in parallel to boost power.