Microphone closest to mimic human ear (not just few inches away)
A microphone can pick up sounds of any level. However, it also generates noise, as does the amplifier following it. Very quiet sounds will be indistinguishable able the noise.
You therefore need to concentrate on the Signal to Noise ratio (SNR) of your microphone + amplifier system. I emphasise system, as there are many sources of noise, and you need to concentrate on reducing the dominant source for any given setup.
For a purely passive electrodynamic microphone, like a moving ribbon or moving coil, the electrical noise of the amplifier that follows it will dominate the inherent resistive microphone noise. You will also have wind noise, and environmental noise conducted through the microphone mounting, which will almost certainly dominate any quantum noise processes.
Different microphones will need different amplifiers to optimise their noise depending on output impedance. A moving ribbon mike has a very low output impedance, and usually uses a transformer to raise the impedance before amplification. A moving coil mike can be fed directly into a low impedance bipolar input amplifier.
If you buy a high output active microphone, then there's little you can do electrically to improve the noise from what it provides.
As Chris Stratton points out, multiple microphones can be used to create a beam pointing at the source. It's still possible to get omni behaviour by create the beam on the fly using clever DSP.