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>>20878 cont.
To actually answer your question, I'm a fan of Convict Conditioning, although I'd add inverted rows to the program. I also like all of Al Kavadlo's work, but most programs will be fine as long as you keep in mind progressive overload.
The basic idea is to try to find a decent balance of exercises and increase the weight you're pushing/pulling by moving to harder variations and, where appropriate, moving from two-handed/legged exercises to one-handed/legged exercises.
There are basically two things to avoid if you're working for strength:
One is endurance focused programs. It doesn't matter how many pushups you can do in a row, your strength won't increase after about 3x20, maybe even before that. You have to move to a harder variation. More specifically, you have to move to a variation that involves pushing a higher percentage of your bodyweight or concentrating that bodyweight on a smaller number of muscles (I.e., working to one-arm pushups with elevated feet).
The other is programs that focus too much on gymnastic skills. Reddit's recommended routine is fine, for example, but its focus involves more gymnastic skills than the ones I mentioned. Those skills are super cool and benefit your over-all athleticism and ability to avoid injury, but anything that isn't going to increase the amount of weight you're moving isn't going to help increase strength or hypertrophy. /r/bodyweight's sacred text, Overcoming Gravity, is a great resource, but there's a reason it puts "gymnastics" before "strength," in the subtitle, and it's the same reason the author, Steven Low, looks the way he does despite being able to perform some impressive feats of gymnastic skill and athleticism.
As an example, ring dips are harder than parallel bar dips for most people, but the added difficulty comes from stabilization and coordination, not from pushing more weight. Also, silly things like one-finger pushups are pretty much just gimmicks.
You can try to master both the gymnastic skills and the strength work, but most people end up choosing which is more important to them and neglecting the other--some gymnastic skills are pretty much impossible if you're too swole.