Slow is smooth, smooth is fast. Work each step until smooth - hand to the gun, draw, presentation/sight picture, trigger pull. Then work them together until it's one fluid motion, nice and smooth, then you'll start picking up speed. Remember that how you first grip the gun to draw it makes all the difference, with the proper grip your sights will line up naturally, without it you'll be making adjustments to line your sights up and that will slow you down a lot.
"If violent crime is to be curbed, it is only the intended victim who can do it. The felon does not fear the police, and he fears neither judge or jury. Therefore what he must be taught to fear is his victim." - LtCol Jeff Cooper