Pullups build up really good functional strength in the back. If you do lever pullups, with your body parallel to the ground, those will work your back from a different angle and your abdominals and hip flexors all at the same time.
In terms of strength, regular pushups are useless; once you can do about 12, you've got all the strength from them you can get. What they are great for is ENDURANCE in your arms, so that if you get into a sparring match, your arms don't wear out on you. If you can benchpress a lot, but only manage 25 pushups, that means you may be able to punch hard in a fight, but if you go into a prolonger boxing match, your arms will tire too easily; being able to do lots of pushups changes that.
But you should have a balance. Learn all the handstand presses, all the pullup variations (the normal ones, the lever pullups which will make people stare
, planches are good, if you get to planche pushups, people will really stare
etc...) and also do all the good lifts and barbell presses, like deadlifts, cleans, jerks, and presses, bench press, THE BARBELL SQUAT, military press, etc......you can also get into things like tossing big weights around, etc.....
Then there's kettlebells, which are different from ordinary free weights as the lifts are different. There is one kettlebell guy who can do full splits and stand in full split (or vertical side kick).
There is so much to strength training.