What are you shooting? (target-wise).
Several folks for sporting like MMS, which means Move, Mount, Shoot - your focus is on the target and is it reaches your insertion point, you are moving your body and gun to that point and then firing as soon as your stock gets to your shoulder; others like Sustained Lead, others Pull Away, and others yet Swing Through. The SMART shooter learns them all and learns when to apply each for the best success. For Sporting and FITASC, at least, there is no "one way" as the targets are NEVER the same, unlike Zippy's and Big Jim's skeet.
One thing I will say about rabbits - as it moves along it slows down, come up to it from behind and as your muzzle (and focus) hit the butt, shoot it as you gently follow through. For dropping targets, (especially incoming and dropping), since they are accelerating, follow the target line and "bow to the target" with your muzzle under the bird; for chondelles, those high arcing ones, either follow the line up and get it either just before or after the peak, or if you must shoot when it is going to be dropping, picture a rectangle and as it enters one lower corner, you swing your gun straight across to intercept it at the other lower corner - if you try to follow the entire arcing movement, you will be behind and over it.