Best way to make a flat looking surface and not have to worry about lighting is to apply a cartoon shader in my opinion. Of course, if you're new to Maya, this might be slightly complicated, but the directions for using it are on my website along with the actual shader if you want to get it.

If you don't want to go that route, try applying a lambert material to your box instead of whatever it has now. (lambert is the default material though) They have the least dealings with light and have no reflectivity. As for your acual lighting, try choosing Create>Lights>Directional and place that in front of your box facing toward it and that might help a little too.

As for animating, it's a lot like flash, but still different. To animate the box:
1) select the frame you want to key
2) select your box
3) press the "s" key on your keyboard. This keyframes your bxo on the frame you're on.
4) select a different frame in your timeline.
5) select your box.
6) move your box however you like
7) keyframe again by pressing the "s" key.
8) play the animation
Now your box will move from one position to the other smoothly.