A sharp mind, relaxed body and a strong back are all you need.  Posture is defined as:  the position of the limbs or the carriage of the body as a whole.  Having good posture while playing drumset is essential.  All four limbs move from the center of our bodies.  Our feet play the pedals and arms and hands play the drums and cymbals.  Any leaning or upper body movement must come from our backs.  How much stress and strain we put on our back depends on how we set up our drums.  Heights and angles of drums and cymbals, tensions of hi-hat and bass drum pedals, height of throne and distances between drums and cymbals can all affect the amount of strain on our back.  I try to keep all distances relatively small.  For example, the cymbals are not too high for me to hit them quickly.  The toms are positioned closely together.  The snare drum is close to the hi-hat and rack tom.  The hi-hat is positioned comfortably so that my left leg is not over-extended.  The throne is positioned so that my thighs are flat as they extend towards the bass drum and hi-hat.  All the drums and cymbals are in a place that is comfortable to my body.  When setting up your kit, take in to mind your own physical attributes and how that will affect your set up with regard to your back. 

One of the best ways to improve your posture, is to increase your awareness of it.  Watch as many players as you can.  See how they sit.  What can you learn by this?  Everything.  Watch players with less experience, watch seasoned pros.  You’ll probably notice that most of the better players have decent posture.  Granted everyone has their own playing style and unique anatomy.   Breathing and posture are related!  Good posture = good breath!