This is the progression roadmap to get you from zero push-ups to a handstand push-up. You should be able to do at least 15 of the prior one before switching onto the next push-up type.
Wall Push-ups
Elevated Push-ups
Knee Push-ups
Wide Push-ups
Regular Push-ups
Staggard Push-ups
Narrow Push-ups
Diamond Push-ups
Power Push-ups
Clap Push-ups
Double Clap Push-ups
Head Tap Push-ups
Pike Push-ups
Elevated Pike Push-ups
Elevated Pike W/ One Leg Up Push-ups
Wall Handstand Push ups Push-ups
Learn A Handstand
Free-Standing Handstand Push-ups