First, may I make a suggestion, please? There is accuracy, and there is shooting to point of aim. You can shoot a one hole group, but if it's six inches low and five inches to the right of point of aim, AND if you own and shoot a fixed sighted revolver, well that accuracy won't do you a lot of good!
Most of my J Frames have fixed sights, especially the ones I like to carry most, and especially for EDC. Now some distances involved with why we choose to carry every day are close enough that accuracy and point of aim are not as critical as longer distances, but we don't get to choose the distances for serious social encounters, do we? And I seriously doubt that you intend to use your J Frame for competition target shooting, unless maybe you are shooting in a match with others similarly equipped.
I like an accurate gun with cartridges that will shoot in that gun as accurately as possible and as close to point of aim as possible. At the same time, for my personal needs, if my gun and the fellow that's shooting it can keep every shot in the bottom of a small paper plate from every distance I shoot it and allow me to do that quickly, it's plenty accurate for my EDC needs. I've had the opportunity to be involved with investigations of shootings much more than I would have preferred, but I do not recall many where the shooter had the luxury of time and a perfect stance to deliver any rounds. Of course, perfect practice toward perfect bullet strikes will help get hits as close as they will probably get under the duress of that kind of shooting.
As has been said, most S&W revolvers were designed to hit somewhere close to point of aim with 158 grain bullets. Some will also do fairly well with 135 grainers and most will also do very well with 148 grain full wadcutters. But different brands and different bullet styles usually shoot differently in different guns. Just because I have found one that shoots like I want it to shoot in my J Frame doesn't guarantee that it will do the same in your gun. But then again, it might be a good place to start.
Today we are fortunate to be able to find a well constructed bullet in several different brands of ammo today. MUCH better ammo is available today than when we only had two or three choices. Since I "grew up" in those times, the primary goal was to be able to deliver whatever you had or got issued to the most important place to do serious damage. Guess what? That's still the most important thing to be able to do.
So my suggestion is that you start by buying three or four boxes of good quality semi wadcutter style cartridges with the same bullet weight and test them for accuracy. Ain't it nice to know that all of them will go bang in our revolvers! So point of aim and then accuracy is what you will be looking for. Of course, if you can afford to do so, you can also try some different bullet weights and see what happens. But while you are doing this shooting, take care to practice being able to fire all those bullets as consistently the same from round to round so you can really tell what potential those bullets may have. Then your search will get a bit more expensive. Remember there are several worthy premium loads, so pick what you like among them and try them. If they shoot to suit you, you probably don't need to worry over much about another brand. Then you need to shoot enough of those rounds so you can send 'em where you want them to hit! Keep it simple. Don't complicate things. Shoot the same gun with the same bullets a LOT and you will be or become someone who can get the job done.
Best part of all, it's a fun trip to take, and when you are done, you will be more familiar with your revolver and you will have developed the confidence in it, in your loads, and in yourself to be able to shoot well ....when you are not under severe stress! But don't lose heart, this is a work in progress, it takes time, and consistent dedicated practice. Just don't give up and don't quit. This situation will work itself out with a bit of time.
I hope I haven't bored you, and I hope at least a bit of what I've said is of some value to you. If it's not, I will not be offended if you just ignore it. But I still say the answer to your question is not as complicated as we all sometimes try to make it. Go shoot some rounds till you find one you can shoot well. You can shoot up the rest of the ones for practice, even if they don't shoot to point of aim. But keep your point of aim where it needs to be and let 'em hit the target where they hit it, hopefully in a decent group at that location! You will know where the rounds will go that shoot to your revolver's point of aim! Good luck, Sir!
