You also need to think about different sections, and what they do. A microphone requires a preamplifier, an LM386 is a power amplifier, and wouldn't be much good fed straight from a microphone.
Assuming you want to feed a set of headphones?, then an LM386 would be fine, but following a proper microphone preamplifier.
There are numerous low-noise opamp's available, such as the NE5532 series - although even better ones are available these days. If you google for such projects a number of them actually use discrete preamplifiers.
The June 2005 issue of EPE had such a project, and actually used an LM386N, fed by a single BC109 preamp from an electret mic insert.