I decided not to employ a separate linear regulator to power the circuit. I did not want the additional source of heat or the possible temperature gradient. Therefore I'll just use a 15V wall adapter as the supply for the entire system. The wall adapter is a switching power supply so I must get rid of the switching noise. I tried several combinations of inductor/capacitor filters and settled upon a 100µH power inductor followed by a 1000µF/25V electrolytic capacitor. A big factor was that I have both of them already in my inventory. 

The LTspice AC simulation predicts the typical 20kHz switching noise to be reduced by about 55dB.