Have you tried the good ol' bouncing ball exercise? A bouncing ball requires an understanding of gravity, timing, and squish+stretch. It might seem stupidly simple, but animating a bouncing ball can be done in so many ways, giving completely different impressions. It's an excellent exercise.
You can expand on this exercise by making the ball not bounce infinitely, but come to a stop after a few bounces. This requires more complex timing, and requires developing a sense for consistency between motions - consistency in momentum as well as material - it would not do to animate the ball as super-bouncy on one bounce, and like a bean-bag on another.
Once you feel comfortable animating a bouncing ball in many ways, you can add in a hand that drops (or throws) and catches the ball, which will require you to practice anticipation and follow-through in addition to the earlier principles, as well as give you the opportunity to apply the earlier principles to something more complex than a ball.