Feeding microcontroller and linear actuators (motors) with the same power supply
I suggest you use a 9V linear regulator as a 'pre-regulator' to power the Arduino through the Vin pin or DC input jack. That way any noise on the 12V supply has to get through two stages of regulation before it can affect the Arduino. 

The Arduino Uno's DC input jack has a diode in series for reverse voltage protection. This has the advantage that the power input can momentarily drop to zero without discharging the input capacitor. The same technique can be used on the pre-regulator. The circuit would look like this:-







simulate this circuit &ndash; Schematic created using CircuitLab

The voltage regulator ground should be connected directly to the Arduino ground, then to the motor driver ground, with another heavy wire going from the power supply to the motor driver ground. This prevents motor current from flowing through the ground wire between the regulator, Arduino and driver, which could cause glitches or worse.