Lowest power WiFi module for IoT
Take a look at TI's CC3200 which was the 1st generation chip and CC3220 which is now the 2nd generation. This has an ARM Cortex M4 MCU and a network processor in a single chip. They have tons of sample code that you can use readily and it has features through which you can set power levels etc. there is a bit of a learning curve with this device though.