That ESP8266 module should be able to connect to a WiFi system. Be aware, however, if it is a 3.3v device, that it will need a lot more current than can be provided by the Arduino 3.v pin.
I believe it is possible to get an NRF24 device that plugs into a PC USB connection. Using a pair of NRF24 devices might be easier, but it would not be as versatile as WiFi. And with the NRF24 devices you would probably need to write a PC program as well as an Arduino program.