How to choose R and C to reduce noise on analog input of arduino?
The ADCs will have a specific maximum input impedance mentioned in the datasheet (for most of the MCUs). Even the recommend series resistor and the capacitor can be found. 
Since the signal is from a potentiometer, it is a slow changing signal. A capacitor of value 10nF or even 100nF at the input of the capacitor will help reduce the sampling glitch. The internal sample and hold capacitor will then be easily charged with the external capacitor.  
The internal capacitor wil be of a very small value in 10s of pF. So, a 10nF or a 100nF External capacitance will not see any loading when the sample and hold capacitor is made to come in contact with the ADC line   
In software, you can employ, moving average as well to reduce the noise further.  
The external R and C together define the time constant. Waiting for several RC time constants (10x or even higher) before reading the value of ADC register yields more accurate result. 
If the potentiometer adds higher input impedance than the ADC expected value, opamp in a voltage follower mode can be used, I'd feasible, bringing down t output impedance of the signal source.