"Minimum acceptable" accuracy for the M92/M9 pistols is, if I recall correctly, a 6in. group at 50yd. This is tested at the factory with pretty much whatever 124gr. ball ammo they can get...from a machine fixture.
Old GI 1911's may not do any better than 12in. at this distance, while a 6in. Colt Python can easily do 1in. to 1 1/2in. with ammo it really likes.
The "key" is to remember that the gun / ammo / and the user are all critical parts of the system...but when people say a handgun is not "accurate", it is almost always the shooter at fault. Damn few people can shoot well enough to actually evaluate accuracy with any handgun or ammunition.
Back when dinosaurs roamed the earth, cops had to shoot 18-24 rounds at 50yd. as part of a 60rd. course. Depending on exactly which course, this included stronghand barricade, weakhand barricade, sitting and prone. Several agencies deleted the weakhand at 50, but some did not. The old B27 target was very generous, and lots of guys could not hit shit out there, but it would surprise you how well some could do. Today, many agencies have actually gone to 15yd. and less for qualification standards. (Hey, if we lower the bar far enough, everybody can get over it!)
When I started...quite possibly before you were born...My first instructor told me to take a gallon coffee can as a guide and draw a circle using a magic marker. Begin up close (7yd.) and when you could keep all shots inside the circle, move back. Worked for me and lots of others...all the way back to 50yd.
Cooper and others have used a similar size target with a time limit of 5 shots in 5 seconds...that is, if you can keep 5 shots on target within 5 seconds at a certain distance, then THAT weapon and ammunition is working well for you...at that distance...for defensive use.
Once you understand proper sight alignment, shooting is actually about TRIGGER CONTROL. Learning to shoot well is hard work and takes serious concentration...but once you master it, it will pay dividends for the rest of your life.