On the first embedded circuit board I ever worked on, the vendor provided a demo by which the LED grew from off to on and back again gently. They did this by using a sine wave, and then mapping the output to the PWM controller mentioned above. At the time, I thought this was just awesome!
Since then, I've discovered that a similar effect can easily be created from a triangle wave and that the sine function isn't needed at all.
Now, I think any beginner should have fun creating a project similar to the "Knight Rider" effect from years ago:
It's an easy and a fun project.