ESP8266

Or you could use the atmega328 for gpio (like an arduino), and use the esp8266 for network traffic.
I connect them together in a small footprint (1.5 inc * 2 inch) pcb, and use the Arduino ide for programming.

My eagle schematic (using 3.3V regulator) is located in the github directory: ESP8266/Schematics/ESP8266Tiny at master · Paulware/ESP8266 · GitHub.

For this purpose the ESP-01 is adequate.