Starting with Arduino in such simple project is possible but yo need to understand the analog circuitry first.
The piezo disc is usually "tuned" to ~ 3 kHz, so it can operate as a microphone for voice and sounds around 3 kHz. Sensing vibrations of lower frequencies need to "retune" the sensor, e.g.by adding a small weight to it. You can glue a steel ball, 0.1"=0.2" to disc center to see if vibrations are detected better.
Following the piezo sensor, a high-input-impedance amplifier is needed, like a FET or opamp. To detect voice frequencies, electret microphones are best, with such amplifier integrated in the case. Microphones lie those are not good in detecting vibrations as their response starts from ~ 200 Hz typically.
As a sound AND vibration sensor you can try a small loudspeaker, best with 32 Ohms impedance or higher.
Use an oscilloscope to adjust the sensor-amplifier output to be sinusoidal (not distorted), with 0.5 V p-p or higher, from your typical sound or vibration input. Only then it is time to connect your Arduino.