No matter how you start or how advanced you are, you can't go wrong using the basic principles/exercises in your training. One of the things I learned early on in my adult life since I was 21 years old is that fundamentals are the key to being successful in any endeavor whether its sports, exercise, business, food & many other things. Sometimes we fall by the wayside and think because something is basic and simple that it feels demeaning and we aught to be more advanced and progressed into greater stages. When it comes to exercise people in many cases believe that the basics don't have any real meaning except as a starting point and then don't need them once they progress to a higher level of progression. Yes its important to keep progressing and getting better but at the same time going back to the basics can aid in your success and not feel like you're Demoting yourself.
The things I learned from specific people in the Physical Culture world is that in order to truly become your own expert is to learn the basics and make them a second language. For example in bodyweight exercise men like Karl Gotch, Matt Furey & others taught the fundamentals of Push-ups, Squats & Bridging as the main staple of any regimen beginner or advanced. In the weightlifting world you stick to basic lifts such as Bench Press, Deadlift, Squat, Snatches, Military Press and basic dumbbell work of those specific exercises which when mastered with good weight will put on muscle, increase strength, utilize multiple groups of muscles and hitting them hard.
I always feel the need to change things up but more and more especially since its not the best weather to workout in, I'm going into more of basic forms of exercises that I can do throughout the day like the last couple days I've been doing Push-ups & Squats throughout the day in Supersets of up to 25 reps in a row. One of those days was doing a total of 300 each which is pretty good considering I haven't done that many in quite some time except the squats. At night I would do my bridging and neck resistance exercise to aid in putting on some extra muscle in my neck and strengthen/lengthen my spine using the Front & Back Bridges holding them for 3 min. each. The squats are Hindu Squats and I keep them even with the push-ups even though the golden rule is to double the squats; this works for me and let's me recover for later sets and as I progress to about 500 each in a day in sets of 25, I will eventually add it to 50 per set per exercise and who knows one day I'll go for 1000 each exercise but until then this works for my structure and my ability to recover. With the Bridging I'll add in the Gymnastic Bridge to get a greater stretch and I do 5 exercises for the neck working it from several angles to build strength and rugged power to keep it from getting hurt and/or pinching it.
The most basic upper body movement in all of bodyweight training is the Push-up and it is the king of upper body movement period. Some call it the king of them all but I a disagree in certain areas of but its highly effective and puts on muscle when you do them correctly. Some put on muscle greater using lower reps, others do so with higher reps. It's been used by countless cultures around the world and was a staple for a lot of Hollywood actors today and more than 50-60 years ago. Men like Steve McQueen, Charles Bronson, Kirk Douglas, Tony Curtis, Burt Lancaster and even guys who played Tarzan such as Jock Mahoney, Mike Henry & the most recent Tarzan actor Alexander Skarsgard used Push-ups to build their physiques for roles in specific films. Seriously if that doesn't inspire you to do Push-ups something is amiss there. The funny thing is basic push-ups are not really enough for some people and try to do variations they're clearly not ready for like one-arm push-ups and plyo push-ups. Don't get me wrong many variations do wonders but there are ones that can hurt you and damage joints if your body isn't in the right setting yet. For me as a big guy at around 270 I stick with 2 arm style push-ups as best as possible and yes I can do one arm and plyo but doing them in high reps is major risk for joint damage and muscle tearing so I stay as basic as possible and have gained results because of this.
Now in terms of how many push-ups one can do, that's up to the individual in what they're goals and intentions are. You are not really competing against anyone to see how better you are or that you can do more than another person; its about training to your fullest potential without risking injury and able to do things on a consistent level. Just because you start off with a low number of something doesn't mean you're a terrible trainee, everyone starts somewhere. I couldn't imagine doing 300 Push-ups or more in a single day when I was a kid because back then to me that was impossible and I could never be strong enough to do that. Not many men my size are doing hundreds of push-ups in a single day since most of them are either out of shape, lifting weights or are strongmen so I'm happy that i'm able to do these and be able to build a physique because of them. Sure I do other things but I'm confident that I'm decently fit for a guy my size. In one workout I did a total of 600 Push-ups in roughly 90 minutes doing Pyramid sets of multiple variations and resting as long as needed. For an advanced person an hour and a half of 600 push-ups sounds pretty weak but I'm not going for records of doing a certain number in a row.
Here's a good solid book of over 60 variations of push-ups you can play with and progress on. Never be bored with dull workouts and be able to train throughout the day or in a single workout your choice. See how many push-ups you can do in a single day and build up to a number you'd like to reach. Make them count. Ultimate Guide To Push-ups