The microwave module you listed should work with ST_Anything as a reglular Motion Detector. It appears that it simply outputs a signal when motion is detected, the same as how a PIR based motion detector works. So, that is good news as hopefully you won;t really have to write much, if any, code to get it working with SmartThings.
As for a starter kit… You could grab the official starter kit from Arduino.cc which comes with an Arduino UNO R3, breadboard, jumpers, devices, and a good tutorial to help bring you up to speed. It is designed for the beginner, and helps understand basic electrical circuits as well as teaches how to program using the Arduino IDE and C/C++.
You can also find numerous Arduino starter kits on Amazon.com.
One thing to be wary of if whether your microcontroller uses 5v or 3.3v. The devices you attached need to be compatible voltage-wise. Often you can use a level-shifter to compensate, but be careful you don’t fry a 3.3v controller with a 5v sensor’s output.