How to build a low noise MIC preamp
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One of the boards has part number SSM2167 so we can easily find its datasheet : where Page 3 reveals(!) voltage noise of 20nV/sqrt(Hz) ... fairly noisy, considering SSM made their name as specialists in high quality audio. I guess it's adequate for some specific purpose, probably in a noisy environment since it includes a compressor. It does work happily off just 3V.
Another uses the AD828 (I note in passing that SSM was bought by AD) which is billed as a VIDEO opamp, with a bandwidth up to 90 MHz! A curious choice for a microphone. Nevertheless its input noise voltage is just 10 nV/sqrt(Hz) ... a little better.
The third doesn't say, but the photo shows a NE5532, which is 5 nV/rtHz, and has been a staple of pro audio since the 1980s (along with its slightly quieter single channel brother, NE5534, as Graham recommends). It's the best of the bunch for your application, assuming the rest of the board is up to scratch, and you can afford to power it (at least +/-5V, +/-12V better).
As mic amps go it's still pretty noisy; I've used the 5534 preceded by a discrete transistor stage to get input referred noise well below 1 nV/sqrt(Hz), when dealing with studio condenser mics. But there's no need to go to such lengths with the electret capsule fitted to your headphones.
The above all assumes the &quot;noise&quot; is simple white noise. If it's something else, buzzing, hum, etc you need to find the cause and eliminate that instead, e.g. by electrostatic screening around your amplifier, and/or improving your power supply.