I am just starting and am feeling dizzy already now I know why, that suggestion of resting for 20minutes seems perfect, because working so hard without rest, wear off energy in our body tissues, ligaments, tendons and leave us with so much stress shown on our faces and body especially for new members like me, so I make adjustments until I find a perfect solution that will propel me to do push up better everyday.
I will suggest since you just started it will be best for you to get started with a lower number of reps and increase gradually as you get more fit and stronger, you can start with 2 set of 10reps like 10*10 in the morning you can as well add noon and evening of two set and 10reps and gradually increase your numbers set/reps as your fitness and strength improve and also eat more proteinous food which will also help increase your muscle mass, just give it a try.