Just a quick video demonstrating some progressive exercises for shoulder strengthening for those who are working towards a handstand push-up. - -
Working your way from the bottom-up will be much more beneficial than just wall handstands and failed free handstand attempts, because you're working the muscles from a full range of motion, learning the movement with stability, which will aid you in the long term with your shoulder strength.
However, you SHOULD work the handstand on the wall as well, practicing the negative motion to get the maximal results. 👍