Microphone to microcontroller

The microphone modules that you listed are different animals which accommodate the wide level range of sound in two very distinct manners:

-The gravity decibel meter module converts the wide audio level range by applying a logarithmic transfer function and outputting a DC level which is proportional to the decibel level. No actual audio output here, only a DC representation. This is only suitable if you want to build a sound level meter.

-On the other hand, if you want a module which outputs an actual audio waveform, for recording, a public address or similar applications, then the MAX9814 is your module. It does have a variable gain amplifier, which will automatically varies the gain to prevent clipping at the output. The module's description clearly indicates this feature... Why are you saying it doesn't have an automated gain control? This is what AGC means.