RE: pistol shooting...
Practice, practice, then practice some more. I would normally recommend dry firing practice but I'm not sure if its good for a buckmark pistol- I shoot a Ruger which has a firing pin stop to prevent damaging the chamber, but .22 ammo is cheap enough that you can afford to plink away all day.
The best advice I can give you would be from my experience with bullseye shooting using a one handed grip, though I'm sure others can give you excellent advice using the combat stance. Buy yourself a small 2lb dumbell. While watching TV at night hold the dumbell out in front of you as much as you can to strengthen your muscles and get them used to holding a pistol weight object. You can even go a step further by carving and taping a grip similar in dimensions to that of your pistol to the dumbbell. Get yourself one of those grip strengthening devices that looks like 2 handles on a spring. Squeeze this to strengthen your grip using all of your fingers except your trigger finger. When shooting, you want a strong grip but with your trigger finger relaxed.
Gte a target that is easy to see. A white paper target with around a 6" bullseye is a good start. Use a stance with your strong foot forward (this would be your right foot if you are right handed) and turn your body about 45 degrees or more away from the target. Concentrate on sight proper sight picture and keep you focus on the front sight, not the target or rear sight. Us a sight picture where the bullseye sits on top of the front sight, don't try to center the sight on the middle of the bullseye. Now for the hard part- squeeze the trigger as the sight aligns with the target. As you already found out, the target doesn't like to sit still, but will become steadier with practice.
Don't forget to shoot at tin cans, tennis balls, clay pigeons, or spinner targets as well. It takes your mind off of getting good groups and is alot more fun anyhow. Fun practice=more practice.
If you are keeping most of them on the paper at 50 ft you are doing better than I did when I first started, I was lucky to hit a sheet of paer at 25 yards half the time. You will get better with good practice. My Ruger MKII is just as accurate as most .22 rifles and I'm sure your Buckmark is just as good- the pistol is capable of very good groups and accuracy, it just takes alot of time to master it.
Alcohol, Tobacco, and Firearms... who's bringing the chips?