I shoot DA revolvers double action about 99% of the time. I only shoot them SA when I want to compare the two, to show myself how well I can shoot DA with a particular revolver.
Gaining accuracy in DA is a result of understanding the importance of trigger control in shooting. Accuracy is about trigger control. Any monkey can align sights, given enough time and incentive. Marksmanship comes from holding them in alignment while pulling the trigger to sear release. That involves being able to move the index finger independently from all your other fingers, and from your metacarpels themselves. It is a learned skill that comes with practice, but one must undestand what he is trying to accomplish to do it.
Rather than concentrating on sight alignment, instead, dry fire with your eyes closed, concentrating on an even trigger pull, same pressure, all the way to sear release. What you want is an even, steady pull to the rear. Not too fast, not too slow. Concentrate on eveness of speed, not the speed itself. Next, balance a penny on the top of your barrel and do the same, eyes open. It's easier if you have a sight rail. Finally, when you can pull the trigger without wiggling the muzzle around, align the sights and do it again. You will find a rhythm to it, that allows you to pull the trigger evenly. At first you will be able to do it well only at one speed, then you simply take the rhythm and speed it up.
You will find the S&W, Ruger and Colt triggers to be decidedly different. There are even differences in DA triggers produced at different times, ie The Pre-war M&P vs the Model 10.
Learning trigger control on the uncompromising DA revolver will benefit your shooting of all fireams. This is why the venerable K-22/Model 17 or 18 is a gun loved by many marksmen, and why it commands the price it does in the marketplace. It allows for a lot of cheap shooting with a great DA revolver, using immediate feedback to develop trigger control.