Microphone pre-amp is a very simple circuit, most all low noise op-amp will be sufficient for this circuit (TL071, TL082, OPA371, NE5534, etc). This circuit will be suitable for dynamic microphone, electret microphone (or a condenser microphone with active circuit inside).
A condenser microphone (without voltage bias source) won’t work for this circuit. If you want to use it, you can add a small resistor about 10kΩ to bias a condenser mic, before entering C1 cap. To do this, just connect the resistor in series with the microphone (Vcc-Resitor-Microphone-Ground), and tap the output from the junction between microphone and resistor to be connected to C1.