re: Shot my new to me 357 magnum today for first time.

For starters, you need to adopt and learn a stance.
Modified weaver is mine.

Too fat of grips, and you do not have enough finger on the trigger to stage double action.

You should be shooting both eyes open, target focus, front sight in the perificial vision. Rear sight almost moot point, but it is faintly in the perificial vision .

Staging double action is when you have enough finger on the trigger, that as you pull back slowly, the tip of your finger bottoms out on the rear of the trigger guard, acting as a stop, at about the same time the cylinder has rolled over & locked.

Once you get good at it, in one fluid motion you are pretty much single actioning a double action.