Oh and yeah ... the moonlight sonata first mov?? Not as easy as you think.
If you want easy beethoven there are the two sonatinas ANh 5.
The rondo from number 5 is particularly cute.
Jump to 1:13 to see the rondo... the dribbling on the piano isn't cute though.
When you've done the two sonatinas there's the op49s.
Start with the second mov of #2
Jump to 4:29
The first movement is allegro moderato, not allegro stupidly fast as barenboim plays is.
Then for something famous, try the adagio from the pathetique, but not until you've done the other four.