I have done a lot of basic tutorials over the last few months, and after learning some things, I am mostly intrigued by servo's and DC motors. I learned through study how to control servo's with a button, and learned how to work with the little DC motors.
Given this, it seems you have pretty much all the tools you need. Can you simply make a sketch that has these four things happening with suitable calls to delay() between them?
Note that later on, you'll want to drop the use of delay, but for your current requirement, it should work fine.