Choosing the ground for circuit
It depends on the rest of the stuff you have.

For example if you have a high-power motor, then it would be unwise to route its ground current through the tiny arduino GND pin. In this case the ground of the motor controller should be connected directly to the battery negative terminal so the motor current does not go through the arduino.

However, for low-current loads, it matters much less.

If you have an analog sensor which outputs a voltage relative to GND, and want to measure it with the arduino ADC, which also measures relative to local GND, then it makes sense to connect the sensor ground to the arduino GND.

Extra credit: read up on common impedance coupling.