Bernarr Macfadden once said "Weakness is a crime. Don't be a criminal." in most cases, he was right but if you ever read the book Mr. America by Mark Adams, there were some questionable things the man did that made you think twice if he was a little off in the head. However; it's important to know that building strength and health can keep you out of a jam and avoid certain unlawful activities when it comes to fitness.
Nobody's perfect and we all slip every once in a while where it can be a workout, a missed meal or go off a program. It's the consistency of staying so called "weak" that can be criminalizing but it's mostly on ourselves. certain things aren't always in our control but we do what's possible to keep things in check.
On that note, when it comes to bodyweight training, the most common exercise in many aspects is the Push-Up. Whether the typical Regular Ones, Hindu Style or Isometric Holds, Push-Ups are the ground work for building strength and conditioning beyond just being an upper body movement. It is a test of control and a test of what you can do with just you alone. They can be done anywhere and can make someone very successful in various aspects of life.
Some only do one format, others learned multiple variations that they can use in their arsenal. You have incredible knowledge at your fingertips on doing types of push-ups that will send you into realms beyond your imagination. That sounded really corny and a marketing cliche didn't it? For real though, it is important to understand what certain push-ups will do within certain muscles in the body because not all push-ups are created equal and that's ok. Some start out with a few and expand to doing hundreds at a day at some point, others may prefer doing a certain amount of reps to get a pump or to stimulate the muscles in order to build strength and then there are those who just like holding at certain points of a push-up in an isometric fashion. However you do them, as long as they don't hurt you or cause harm to the shoulders and elbows, you can have great success.
Train to what gives you the best benefit. That's the true nature of the game. If you want to go nuts and do hundreds of push-ups a day, go for it if it helps you stay strong. Just remember, doing that is just one aspect of the puzzle, it's not the only way to results and not everyone is meant to do hundreds a day. There are people who do have joint problems and doing tons of push-ups can make things worse so find a solution that doesn't make you feel pain in your joints. Hell, most of the time these days, I'll do no more than a couple hundred myself and that's it, other times, I'll do my 1 minute push-ups where I hold the top for 30 seconds, then hold at parallel and not touch my chest to the floor for another 30 seconds. I'll repeat this kind of push-up for several sets. In some workouts I'll superset them with a 1 minute Horse Stance and do up to 5-7 supersets.
The most push-ups I've ever done in a workout was 600 doing different variations and could do 250 doing a deck of cards with Hindu Squats. I like doing Fingertip Push-ups from time to time and like the Mishra Dand style in honor of the ancient wrestlers of India. Find what works for you and kick ass in it. I believe in you and you fucking got this. Be amazingly awesome.