Hi Lisa,
For my first melonJS game, I used Chipmunk-js for 2D physics. It worked really well. I can't comment to Box2D, but I know it is also a popular 2D physics engine available for JavaScript.
Finally, I have two games that use the above code, both with source code available:
Your question about the game mechanics is more of a question that could be answered on the Chipmunk or Box2D forum, since the answer will relate to how you use the physics engine, and not with how the engine itself integrates with melonJS. We can help you out with the integration part. But I would have to defer physics-related questions to the appropriate forum.
Either physics engine can work with melonJS, but integration is not as easy as it could be. Chipmelon helps out quite a bit if you're using Chipmunk-js, though.