The way I would recommend getting started with Java GUI programming is with Oracle's Java Swing tutorials
(or a good book if you have access to one).
I would recommend getting familiar with creating simple GUI interfaces (buttons, labels, custom painting, etc.) before attempting something like an animation.
The animation part can be either difficult or easy, I would recommend starting out with a series of still coin shots and simply switching between the pictures. If you're feeling ambitious, you can try 3D animations via JOGL or LWJGL (jMonkeyEngine might also be a viable and easier alternative).
I've never personally used BlueJ, I'm kind of an Eclipse fan myself
Another good IDE is Netbeans. I believe all three are free (Eclipse and Netbeans are open source, not sure about BlueJ).