Breaks between sets
Breaks between sets are set in order which optimises the effects of the training. If you want to change the order of the breaks, you can do so, but we have a couple of suggestions for you.
Length of the break isn't that important in the beginning
If you do less than 51 push ups, breaks between sets aren't that important. If you want to you can even extend them a little. The most important thing is that you should do push ups precisely.
If the sets don't exhaust you enough, you will use the rest of your energy during last set in which you have to do as many push ups as possible. Your muscles will continue to grow.
The length of the break is important above 51 push ups
At this stage the training changes. Your muscles are quite strong now and you do push ups more easily. Sets become shorter but their number grows. Now we start to develop endurance of muscles. It will help you in reaching the 100 push ups.
If the brakes are too long you won't develop endurance. Of course you will eventually reach 100, but it will take you much more time.
Remember though that if at the end of a brake you still feel exhausted, rest longer and wait until your breath calms. Everyone has his own rythm and should train according to it.