How to make an SMS notification to my phone with Arduino Uno?
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.