Resistors between Arduino pin and transistor
R9

The resistor is here for current limitation. In your application, you want the transistor to switch on when the arduino pin is HIGH. To calculate that resistor value, you have to how much current will flow across the transistor when saturate  (\$I_c\$). You can then determine the needed current coming from the arduino to toggle the transistor : \$H_{fe}=\frac{I_c}{I_b}\$ with \$I_b\$ the current delivered by the arduino. Knowing \$I_b\$, you can determine the resistor value.
R10

This resistor is here to set a default value a the transistor's base, commonly called "Pull Down resistor". When the arduino is just power up, pin's voltage level is uncertain, that's why you need such a resistor.