Get a pair of BB guns. A long gun type BB gun will teach you sight picture quickly and very cheap. You may be able to borrow one. This education on sighting is easier with long guns as the weapon is more controlled by both hands over a distance rather than both hands clasped around a grip on a handgun. This will also show you if you are flinching due to expected noise or recoil. When your good with the long gun move to a bob handgun similar in shape and feel to your real weapon. Use what you learned with the other BB gun to be able to line up sights properly. Now you must simply learn a good shooting stance with the handgun. Eliminate flinch by slowly pulling trigger until it surprises you when it goes off. Control your breathing and make sure you do the same thing each time. Sight the same, breathe the same hold the weapon the same. Make a list to recite, left hand,right hand,trigger finger, breathe, bang. Your groups will tighten up with the bob gun and then go back to the real weapon. All you have to do now is use the education you gave yourself with the BB gun.
And even with BB gun, small targets are fun and challenging. I learned with toy soldiers and soda cans. Cans at longer range with the rifle. Soldiers a bit closer with handgun. Focus will force your shot groups smaller and smaller.
Even if you buy new BB guns, you will get more use from them than many other guns because you can shoot a lot of them at home...weak ones inside the house if your extremely careful. Plus a daisy cheapo lasts forever and is 40 bucks tops, and the handgun version you could even go airs oft and stay under 20.