Just my 2 cents, but when i started several months ago I couldn't do one push-up, not even a knee push-up.
Wall push-ups seemed too easy so what I did first is knee push-ups where the knees are on the floor but the arms are on a low couch. That seemed to give a good angle. After then progressed to knee push-ups, then full push-ups.
Now I can do 20 push-ups straight or 40 in two reps, and thats while weighting about 220lb. You wouldn't believe how fast you progress on these things. The key for me was average load on the arms with many reps and keeping at least 2 under failure.