Questions about motors and motor control would best best asked in the Motors, Mechanics, Power and CNC category. In fact, it may be better to keep the whole project within the same thread for continuity,
if fact i am already thinking of stepper motors with lead screws (just an example). Add an Uno with a CNC V3 shield for the controller, The CNC shield has connectors to make it easy to connect motors, limits switches and other sensors and actuators. Lead screws resist being back driven so no need for brakes and such on the legs.