THAT Corporation produces a range of specifically designed ICs for high performance microphones as used in live sound, broadcasting, recording and conference systems. We recommended the THAT1583 and THAT1580, which are compatible with the range of gain control ICs where remote or automatic control is required.
The 626x series is an all-in-one solution, ideal for portable or USB powered products where low power is a key requirement, as just 30mW of power is needed. These parts are also very low noise (-126dBu EIN) and are digitally controllable.
Very low noise op-amps are also popular for microphone preamplifiers. The NJM2122 and NJM8830 are a good choice.