I can't address bestness. I've gotten good results with an [Edit: Fix this part number] SSM2166, "Microphone Preamplifier with Variable Compression and Noise Gating," from Analog Devices. Here's the datasheet.
The device looks like it's intended for use with an electret, probably in a mobile phone. It advertises a maximum compression ratio of 15:1, expressed in dB. In the compression region, a 15 dB change on the input yields a 1 dB change in the output. At maximum compression, a 40 dB input range translates to a 2.7 dB output range; a range of 10 millivolts to 1 volt translates to an output range of 0.74 volts to 1 volt. The degree of compression over most of the range is set by an external resistor; at the high end of the input range, it's 15:1. The IC also has a setting for a minimum signal level, below which the output drops off dramatically, so the compressor won't try to boost background noise during quiet periods.
The IC has four operating parameters that are set with external resistors. This post will be too long already without describing them, so I'll refer you to the datasheet. The datasheet recommends using potentiometers in the design phase, and determining the external resistors experimentally, suggesting that the settings interact so much that it's not feasible to provide formulae or charts to describe those resistor values. The datasheet shows charts for specific settings, but my experience says that a slight variation from those settings will change the device's response to the remaining settings quite a lot.
The datasheet shows a schematic for an evaluation board with four three potentiometers, and gives instructions for determining external resistors by experimenting with those potentiometers. I built the evaluation board, and the procedure worked well for me. When I switched to fixed resistors, I got the results I expected.
The evaluation board takes three potentiometers, seven capacitors - four electrolytic - and seven fixed resistors. The final product needs the same components, less the potentiometers. I built mine with tantalum capacitors on an Arduino protoshield. The IC is in a 14-pin SOIC package, which the protoshield accommodates nicely. I used tantalum capacitors for their small size and height, which will matter if you want to stack yet another board on top.
I've used this IC for reading inputs from musical instruments, and it's done a good job of keeping the signal voltage at a usable level while the sound level from a plucked string decays. I haven't used it for voice. It's pricey: 6.68 USD in singles from Mouser. But, it does a lot of stuff.
An alternative might be SA575. I've never used it. It advertises similar capability, but doesn't seem to coordinate all its features like the SM2166. It seems to leave more work to the designer. Mouser still has about 40 of the through-hole version available, if that matters to you.