The FBI only began carrying firearms in 1934, legally, at least. So they were late in the game. Prior to WWII, shooting stances were rather dueling oriented, at least on the range. That was the way it was taught in the army for ordinary soldiers. Fairbairn's techniques developed in the Shanghai Police Force were adopted (or adapted) by Rex Applegate, who wrote extensively about them in the 1950s. Part of the idea behind the Fairbairn and Applegate methods was that the trainees would be receiving only a very limited amount of training in the use of handguns before being sent off to war. These days we know that is entirely inadequate, since it is obvious that all of one's handgun skills will be lost within a two week period if at least 100 rounds per week is not expended.
Along the way other fads appeared. One of these was the idea that single action shooting was much more accurate than double action shooting, which seems to be an idea carried over from the target range. While the idea makes sense, it may have failed to take into account certain dynamics of a gunfight. However, a typical police sidearm of the 1950s was a S&W .38 Special with target sights, like the K-38. The latest thing to have would have been a "Combat Masterpiece" that had a four inch barrel. That was followed by the Combat Magnum, later the Model 19. Along with the target sights, it was fasionable to have a target trigger and a target hammer. A nice "bolt-on" modification that was no doubt considered a necessity was a trigger shoe.
