For your first steps with ESP8266 and Arduino, you can use a setup like this:
ESP8266 will need up to about 250mA for short times, the capacitor will help to "jump over" 
The two resistors will bring down Arduino's 5 Volt TX to acceptable voltage for the ESP RX pin (voltage divider).
Sooner or later you should get an appropriate power supply for the ESP. The one in your link may work if you have 5 Volt around.
But the ESP is often used as "standalone" (without any Arduino) because it is a powerful chip (fast, much flash much RAM, compared to most Arduino boards) and it can be programmed directly with the Arduino IDE (for core see: GitHub - esp8266/Arduino: ESP8266 core for Arduino).
So you need a power supply anyway.