The Colt factory test targets I have seen are printed with information that states they are shot at 15 yards with a 6 o'clock hold. They used "standard" loads in each caliber. For a Detective Special that would have been a 158 grain lead round nosed bullet, standard velocity.
Shooting that type of bullet with the same sight picture should result in bullets hitting 2"-3" above the point of aim.
If your question is which load to use in your DS to hit point of aim, the suggestion to go with a lighter weight bullet is a good one. If your question also involves which bullet to use for self defense that will hit point of aim, Speer makes a specific .38 Special + P load that is designed for snubby revolvers with the Gold Dot hollow point that has a good record in actual shootings. Other makers also have "premium" .38 Special self defense loads with bullet weights typically around 110 grains to get the speed desired. They would be worth targeting in your gun to see what teh point of impact is.
As far as effectiveness ? You could easily spend several hours watching YouTube videos. The best ones are when the shooters actually provide chronograph data and shoot into ballistic gel showing penetration and expansion. Most of the newer premium self defense HP loadings for the .38 Special do pretty well. The SWC and SWCHP bullets tend to penetrate a lot more if that is what you are looking for and there is something to say for that trait if you are carrying in an area where assailants are often wearing heavy winter coats and multiple layers of clothing.
