If this is exceeded for more than a few seconds the motor will overheat and be destroyed.
Note that the current is determined by the load, and represents torque.
The motor voltage relates to speed. The power reduces as the speed reduces, because the maximum torque is constant.
If very inefficient motors like like toy motors are used, these characteristics are masked by the losses.
Another source for motors is window winder motors from a car.
All these motors tend to be used as servos for an arm, which means position servos, because they move to a particular position according to a control signal. Another kind of servo can apply a particular force (gripper). These can be combined. Sensors are used with feedback control to do this.
Probably the simplest and cheaper approach is to use a servo motor intended for radio controlled models. You can look these up to find more information, like how to control them. They come in different sizes and are specified for output torque and speed, and run from a 5 to 6V supply.
Generally you need some sort of computer operated interface to run the arm itself, which connects to a PC by USB or similar. Software in the PC performs higher level functions like displaying and keyboard controls, and maybe calculating angles etc. Arduinos are popular in this interface role, probably sufficient to get started, where there is just a few motors. They need to interpret commands (probably from a PC) that drive motors to the desired positions.