We have a lot of members who are big into Arduino - like Brad, Allon, Mark and Salva... Many of these members can give you a quick start into developing for Arduino if you just ask.
The ESP8266 is a new and popular wifi module that can also be programmed like an Arduino! Look for the ESP8266-12. It can be found mounted on a board with 1/10" centered pins (the module itself has no pins.) You will need an FTDI cable that works at 3.3V, and a 3.3V power supply, to program it.
The ESP8266-01 (aka ESP-01) only has a few pins available, but is dirt cheap.