While this may seem like just another thing that’s added to your plate, make copies of all of the keys prior to you move. In all of the chaos of the move it would be easy to lose a key, and that is the last thing you want to deal with on your moving day.
Be sure to research what doctors are in your new state, and whether they take your insurance.
While packaging you should keep important things separate from everything else. Be sure to keep these in your car or somewhere accessible so that you don't need to stress out during your move.