Shoot - NOW!
I should start out by stating that I am not an expert at all when it comes to self defensive handgun use, but I have learned a few lessons from handgun shooting, and particularly competition speed shooting that should be considered.
Common sense will tell you that getting a center mass hit on the bad guy before he gets a shot off will greatly improve your chance of survival. Trying for the perfect shot that takes out his third shirt button might be good marksmanship, but if you try for the perfect shot you may never get the shot off at all.
In this short video I demonstrate taking the first shot as the gun is moving up, rather than allowing the sight to settle on the target, getting a good sight picture, and squeezing off the shot. Yes, this is a race gun, a red dot sight, and a race holster. The technique, regardless, is basically the same. Saving a half or even a quarter of a second can make the difference as to who gets to assume room temperature at the end of the day.
If you want to try this technique, (assuming you have already developed basic handgun skills) use a fairly large target at close range. Start with the handgun aimed a foot or so below the target. Smoothly raise the gun, and break the shot just before the sights reach the middle of the target. The key here is smooth, not quick, and not jerky! Don't jerk the trigger, keep it smooth. You might be surprised just how accurate you can become. Dry fire practice? Absolutely!
Be safe, have fun!