What are your goals? Pulling strength and leg strength aren't addressed by your post. Handstand push up and planche push up are good goals, but you need to know how to get there. Simply doing static holds and working sets of 20+ push ups won't get you there. Get "Building the Gymnastic Body" by Coach Sommer and learn the moves to get you there. Pseudo planche push ups, L-chin ups, straddle L, etc. are intermediary steps to your overrall goal.
Joint prep, strengthening of the weak muscles(external rotators, scapular stabilizers, etc.), working strength (5 reps and fewer), and making a proper routine with good frequency, recovery, etc. are all needed to achieve the goal of (proper) planche push ups. Read up on the gymnastic bodies forum about prehab and joint prep.
Your worksets in an intensification cycle should usually be 5 reps or fewer per set. A strength routine would be 5 sets of 5 reps followed by 3 sets of 8 reps as an assistance move.
Alternate intensification cycles of 2-4 weeks with accumulation cycles of similar time length. Use Escalating Density Training, Bryce Norton's 50/20, etc. for this cycle.
Learn about Charles Poliquin's Undulating Principle of alternating intensification with accumulation.