I was going to start doing the circuit from the RM training tool to help improve my pushups. I currently max out around 20 so would doing sets of 15-20-15 be helpful or should i start on 10-15-10 and work my way up?
Roy - If you can do 15 - 20 -15 then do that, if not then try 10 - 12 - 10 and work your way up gradually. The important aspect here is the pyramid style training which not only assists with strength but also stamina. If you max out on 20 at the minute then you should have no problems doing 15 - 20 - 15 because the RM circuit of which you speak contains 8 exercises working the torso and legs, not just one part of the body. Therefore, by the time you get around to your 2nd and 3rd sets the muscles worked during the press-ups will have had sufficient rest for you to be able to push out the required number - the PTI's designing it know their onions!
In addition to the RM Circuit I added 3 sets of burpees. Maybe you can start 10 - 12 - 10 with these exercises which, IMHO, greatly assist in both developing leg and upper body strength and stamina, ultimately leading to a greater endurance when it comes to press-ups.
It might also be an idea to blast out 3 sets of 10 a couple of times over the course of a day as well as doing the suggested circuit (have 30 seconds rest between each set) i.e. say to yourself evrytime I enter my bedroom I'll blast out 30 press-ups for example. You'll soon find your capacity increasing and you'll eventually start to push yourself harder i.e. "I reckon I can do 3 sets of 12 next time I enter the bedroom". Determination, patience and discipline will get you where you want and need to be.