Picking the right MOSFET
I settled on the IRFZ44N, now the question is am I correct in this
assumption?

The IRFZ44N is going to be a poor choice for this device: -

The data sheet graphs don't even bother going down to show results at 3.3 volts between gate and source because the gate threshold voltage might be as high as 4 volts and this is way beyond the logic level you are considering applying to control it.
Look for a MOSFET with a maximum drain-source voltage of around 15 to 20 volts is my advice - they are much more likely to be suited to your application because they will have naturally lower on-resistance and many will be suited for low level logic drive voltages.