What is a good circuit for recording a piezo contact microphone or an electric guitar pickup?
The LM108 is an old part, and the 30 pf capacitor is required for stability, especially at low gains, and as @Brian Drummond states this has a gain of 1.  A more modern op amp will probably not require external compensation.

In answer to your question, the circuit's response is almost independent of the piezo characteristics in this circuit.  This is because when the piezo voltage increases, the output tracks it and the voltage is pulled up to equal the piezo voltage by C1.  Since the voltage is the same on both sides of R2, there is no current discharging the piezo device.  The frequency response of this circuit is therefore determined not by the piezo characteristic, but by the RC time constant of C1 and R1.  You may even want to make this time constant a little faster - right now it is 110 seconds (less than 0.01 Hz), way below any bass requirement.  Also, be careful with layout because the impedance is so high that the circuit will pick up any hum.