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Well that's incredibly vague. What are you doing with your handgun? I presume you are looking at revolvers, yes?
As far as the wild west goes, I'm pretty sure your average 19th century cowboy didn't much care. He would probably have a short one for his pocket and a long one if he wanted to hit something, what the measurement was was likely inconsequential. I would guess that most "long" revolvers had barrels 5"-7", and snubbies 1"-3".
They come with the rest of the gun. I just buy what seems nice...
Barrel length has been proven time and again to have little to do with the accuracy of the bullet that passes through it. The only thing affected is velocity to a slight degree.
What longer vs shorter does is more about the human interface. Short barrels have shorter sight spacings and that means that slight visual errors in the sight picture produce wider impact spacing at the target. Longer barrels with longer sight baselines are a little more forgiving of slight sight picture assymetry.
But if you focus on the correctly symetrical and proper sight picture you can shoot well with any barrel length.
If you take part in the various competitions where you start by drawing from a holster a shorter barrel clears the leather or Kydex a little faster and with less arm and upper torso gymnastics.
It would be interesting to review the old Colt and other maker's records to see what sort of barrel lengths were sold the most per area. My initial inclination was to suggest that the long barrels were sold the most for the big open spaces. But that may not be the case.