Simple robotics project

I would like to make a battery powered motor spin 360 degree each time a button is pressed as part of a basic robotics project.

The project is very simple:

(1) I press a button; and
(2) the motor spins 360 degrees, rotating a shaft the motor is driving (ie turning it one full rotation).

There are a few things that I need:

- the design must be very tough and shock resistant (eg capable of off road jumps at high speed);
- it must be waterproof (eg if it’s submerged in a puddle it must still work);
- ideally it must be energy efficient (I’m not sure if that means a stepper motor is less viable, but it seems like a logical choice);
- the 360 degree rotations must be precise (eg +/- 5% accuracy at most, preferably less);
- the motor must be somewhat powerful to drive a shaft;
- the rotation must happen as quickly as possible;
- it needs to be relatively compact (as small a footprint as is possible, taking the above into account); and
- it must be reliable.

I need help with the design and coding (if any), as well as selecting the button, the batteries and the motor.