The ESP8266 Wi-Fi Module is a low-cost Wi-Fi radio with a microcontroller on board. Costing less than $5 US, the ESP8266 brings connectivity and programmability to any “connected project” such as temperature sensor monitoring or aquarium control.
The ESP32 module is a MCU with integrated Wi-Fi and Bluetooth connectivity for a wide-range of IoT applications. I recommend the HiLetgo ESP32 module to get started with the ESP32. This will allow to use the Arduino IDE to program the module over USB and leverage your existing experience as you learn.