Aurduino Smart Wifi Wall Socket
The hardware you have chosen is perfect for the job at hand. 
But what @Hapi also mentioned was that you could probably do away by not using the Arduino !
The ESP8266 is in itself programmable. There are many Firmwares available to help you do so. (You can even program your own)

This can help you getting started : http://randomnerdtutorials.com/esp8266-web-server/

This is something like what you need at the end : https://hackaday.io/project/4562-esp8266-wifi-smart-garage-door

One thing to note : ESP8266 works with 3V, while your Relay would require 5V.
Happy hacking my friend.