I have only owned a few revolvers, the only S&W being a Model 60, so in not as familiar with the dash system as I'd like.
The dash-system gets it's most confusing to folks when they try to compare one model's "dash" to that of another model. That doesn't work. The dash means the model went through what S&W considers an "engineering change" which all by itself is a bit confusing or annoying, because sometimes it seems like a small change results in a new dash number while a -BIG- change did
NOT, so go figure. But a Model 60 (just for example) had a royal slew of dash numbers, where some other revolvers (say a Model 586) had a paltry few.
So if you are looking at a Model 19-3, we know we are talking about a 1970's era K-frame. But a dash-3 in a Model 19 is nothing WHATSOEVER anything at all, in any way, like a dash-3 of some other model, even if the models themselves were similar in many or most ways.
I probably didn't explain that well.

Bottom line is that dash number -IS- important, but only important to that model. Don't try to compare a 60-3 to a 19-3 because it's like comparing apples to Buicks.
I know the pinned barrels are supposed to be of higher quality (although it might not be necessary.)
The pinned barrel itself, or the pinning of the barrel doesn't say to many or most that this particular "part" is of higher quality, but what it DOES say to many of us is that the gun itself comes from an earlier time, when S&W did things a different way than they do now. Many have made fine arguments that some things (many things?) from S&W are made as good or even better
now than they did before 1982 or 1983, which happens to be when pinned barrels became history.
I'm of the camp that Smith & Wesson revolvers -WERE- better in earlier times, but I realize that I don't know everything and others have very valid opinions and experiences. But I do know (for sure) that older Smith & Wesson revolvers make me happier than newer ones do, so that's what I tend to chase. A "pinned" barrel is just a quick visual clue that it's a pre-1983 gun, which gets my interest.
The recessed chamber seems to be the other big thing. Is blowing out case heads a problem people have had? Which dash model was the last to have recessed chambers?
Again, it's not a "which dash" as it's a different dash across the line, but only the Magnums ever had the recessed chambers, and nobody has ever proven (or even attempted to prove, to my knowledge) that they offer, well, ANYTHING over the modern, non-recessed chambers. They are *neat*, especially if all your experience is without them... and then you get your first one!

They are a little more annoying to clean. In the real world, they don't really offer any tangible upgrade and simply cost S&W more to make, so they ceased the recessed chambers.
So if all your concern is with safety, I can say you can put that one to rest, there exists no safety issue with or without, or with regards to recessed chambers.
I have owned two different Model 19's, a dash-3 and a dash-4. My dash-3 is one of my favorite guns and I got rid of my dash-4 because of it. In the case of these two specific revolvers, there's no doubt my dash-3 was better in every way. But I'm quite sure I could find another 3 & 4 and get the opposite result.
If you want a Model 19, start lookin' at them every where you go and pick them up. Read
Jim March's "revolver checkout" that is a sticky topic at the top of this forum to help you make your purchase. IMO, for what you are looking for right now, the dash number is of precious little consequence; you simply need to find a good Model 19. I'm sure if/when you do, you'll be thrilled with it, as the Model 19 is
magic! 