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plankton
With RPi most people use a USB Wifi dongle, those are dirt cheap, but not sure how easy it would be to implement support for that (drivers, USB A port)?
First you need to write the USB host driver, then the specific Wi-Fi dongle driver, then the Wi-Fi helper user space utilities, then the Wi-Fi protocol support, then the TCP/IP stack. Easy... not!
The WiFi daughterboard that dc42 mentions includes a dedicated MCU with all this already programmed and debugged... however it costs almost as much as an OctoGoatBox.