If the back is bothering you when doing overhead lifts than put one leg back (or forward...whatever makes you happy) a bit. Gives better support and less stress on the back it's self. Lot of guy's hold the knees too stiff when pressing. A slight bend reduces a lot of stress on the back. Keep the weight directly overhead at the top position. A lot of people don't. Which again, put's extra stress on the back.
Cleans are a mass builder. So are Hi-pulls, which are done with a wider grip. That wider grip affects the laterial delts very strongly. Rear delt's also. Push presses (bar resting on the heels of the hand) and jerk presses (slight knee action/dip to start the press) can also be included, from time to time, in any pressing workout. Preformed best when using a power rack.
A guy from Italy once taught me the value of pressing when sitting flat on the floor, legs out in front of the body. Not the same as sitting while pressing. Main focus was on pure pressing power and core strength from the lower back and ab's. Took any help from the hips/legs out of the exercise. Usually used DB's (one or two arms) for this movement but BB's were used at times. Could also clean from this position, which is a whole new element to core training and raw power. Another exercise was cleaning and pressing while on the knees. Whole different muscle involvement and feel from this movement. Great power and size builder. Good Luck.