I tried using a circle, and found I was doing more of a lazy figure 8( Turn the "8" 90 degrees, on its side). So, I gave up trying to do the circle and went to a straight small-arc, pendulum swing, that I narrow as everything lines up.
As for handgun shooting, I do a lot of 2-hand hold shooting, both for combat, and long range shooting. I also use rests, or creedmore positions using my legs and knees to support my gun for aimed fire. I use traditional 1-hand pistol and revolver shooting to knock the rust off my basics, usually using a .22 rimfire for this purpose. It takes recoil out of the picture so I can concentrate on other aspects and fundamentals. I have a large, heavy pistol( Remington XP100) with a scope on it that really helps me relearn how to grip my handguns properly, and that transfers nicely to my other, open sighted guns.
Those are the techniques that have worked well for me. My brother is more the target shooter, and is a certfied pistol coach. He spent several years on a pistol team using very fine target pistols to shoot bullseye. We talk about any new book he finds that gives another good idea about training.
I am finding that once I knock the rust off my fundamentals, the faster I can get that shot off, the more accurate my shooting is. When I try to concentrate too much on breathing, hold, and squeezing the trigger while holding the sight picture, that is when I get fliers. This is a recent discovery, so I am still trying to explore this idea. It first cropped up shooting IPSC doing double taps, and then again shooting a 48 rd. Ill. Police Association silhouette shoot, when I Double- Actioned my last 6 rds. at 7 yds in less than 2 seconds, and shot all 10-Xs ! The officer next to me complimented me on my "Machine gun shooting"! I was running out of time. In fact, my last bullet cut an oblong hole in the X ring as the targets were turning.