Engineering approach to choosing a motor, voltage and gears
Selecting a motor for a given application requires determining the torque vs. speed characteristic curve for the driven load. How much torque is required to overcome static friction and get the load moving very slowly? How much torque is required for steady operation at any given speed up to the maximum operating speed? Those figures are determine by the friction of the driven equipment and the work done in the process. Then the inertia needs to be determined. The torque required to accelerate the load is the friction and work torque plus the torque of mass X acceleration. That is all mechanical engineering.

To select a motor, you need to determine the toque vs. speed capabilities of available motors and find one that meets or exceeds the torque vs. speed requirement of the load. You need to know how to interpret motor specification sheets and convert the data to speed vs. torque curves.

Many applications require only a means of starting and stopping the motor based on the requirements of the driven equipment. Small motors can simply be turned on and off. They will accelerate based on their capability and the requirements of the load. The load will coast to a stop when power is removed from the motor. For some applications, simply turning the motor on results in acceleration that is too stressful. Acceleration can be controlled with an electronic speed control (ESC). Some applications require speed control for process or energy saving reasons. Brushless DC motors require ESC because of their design. Brushed DC motors larger than a few hundred watts require ESC to control the starting current. AC motors may require a soft starting system or ESC depending on the capability of the source to provide starting current.

The above is a summary of the basic considerations. There are a lot of approaches to learning the details. I recommend looking to see what is available and determining what is easiest to understand.