How to make an SMS notification to my phone with Arduino Uno? I am planning to make an SMS notification to my phone with Arduino Uno via a push of a button.

I have an Arduino Uno C520A Embedded System. Is it possible to do so with this model ? If yes, which WIFI module should I get ? 

I just want to make an API request to the web through the push of a button.
It is possible if your provider has a sms gateway e-mail-address. Just google which it is for your provider (e.g. number@tmomail.net for T-Mobile (US)). And there should be a lot of tutorial about how to send an email with an arduino.

Every wifi-module with arduino support will work if your WiFi is a standart 3.6Ghz. And yes it should work with any arduino compatible microcontroller.