You can modify and progress in your push-ups by starting with a version that reduces the amount of weight you are pushing: the higher your hands are elevated, the easier the push-up is.
From easiest to hardest, push-ups progressions are:
hands on wall
hands on kitchen counter
hands on seat of a chair
hands on high step platform or step (you can start with more risers, then eliminate risers as you get better).
By progressing like this, on your toes, you will gradually develop strength in the muscles needed to do full push-ups. But don't be discouraged if you still end up doing some, or all, on your knees.
A push-up done on the toes is equivalent to lifting 75% of your body weight. Done on the knees, it's 65% of your body weight. Not a huge difference, IMO.