Proper stance is an important element of shooting but to be honest it is way over hyped and over-analyzed. This I can tell you in general: the modern isosceles stance is what the vast majority of good shooters use currently. The Weaver stance and those variations are limited in their mobility. If you currently use weaver, up to you. However, for the new shooter, I suggest working with the modern isosceles stance as the default.
In terms of discussing “shooting stance” I prefer to use the term “shooting platform.” What this suggests is that the actual way you are standing does not matter very much as long as your body is creating a solid platform from which to effectively shoot. How solid this platform will be is situationally dependent. What if you are on your knees, what stance is that? What if you are knocked to the ground, what stance is that? What if you are running with a small child in your hand and firing on the move with the other? What stance is that? I bet those circumstances would not fit neatly into any “shooting stance” that you have been taught.
We need to train to the point that we can maximize our platform under any given circumstance to make our shooting as effective as possible, given the circumstances. With that said, people are always interested in a default shooting stance. My advice is simple on this: stand like you fight. You may not consciously know what that means, but your body innately knows how to stand when you fight.
Think about this: in your youth when you played football or any such vigorous sport in the back yard with friends, when a kid on the other team came at you full-force and full speed, about to slam into you, what would you do? Instinctively, without even thinking about it, you would lean into the impact, weight on balls of the feet, not heels, and you most likely had your arms raised, hands around head level, palms forward, fingers splayed. One foot would be slightly ahead of the other to maximize balance, yet your upper body would be facing the incoming attack square on to maximize your power. That is how you would instantly stand when bracing for that impact, unless you are a freak of nature unlike all other humanity. This is how we stand when we fight and no amount of practicing to do a “Crane Stance” or any other Kung Fu bullshit will overrule this natural fighting stance when you instantly react to a threat.
Since this is how your body fights this is also how I suggest you stand to shoot. While I love competition shooting my primary concern is as a defensive handgunner and if you do bring the gun into action from a starting position of just standing still (rare in actual fights) you are going to be facing a threat in that position. Your body will ensure that. Therefore, stand like you fight, because you should practice technique that works with the body’s natural tendency, not against it. As it turns out, the modern isosceles shooting position, used by all top competitors, is essentially this natural body stance. This is also the standard “non-confrontational” defensive stance that any serious combatives instructor will teach you as a default fighting stance. See how it all works together now? Why work against this natural fighting stance in your shooting? If you need to use your gun to defend yourself you will certainly be in a fight. Therefore, stand like you fight.