Here is a tune that I learned fairly early on, from the excellent instructional video by Denis Pepin (out of print). I can't recall the name of the tune, and because I don't have a VHS player set up, I can't simply refer to the video. The tune is traditional.
In the recording, I am playing a Melodie in D with only the clarinet reeds (MM+) for clarity.
And a direct link to the MP3 here.