ESP8266

Very low cost, low power, wifi enabled, 32-bit microcontroller for IoT applications

Power Consumption:

http://bbs.espressif.com/viewtopic.php?t=133

ESP-01

These are the correct way to connect the ESP-01 to the breadboard. The second has a parts list, mostly direct from manufacturers. All I really need is the capacitors for the second (preferred) layout but having the special connectors for the breadboard will make it much easier to view the connections.

I should also look for more pre-cut wires of different colors than what I just bought.