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

Nothing beats practice.
A smaller gun with a short barrel is meant for close in work so if you can keep it on center mass at ten years then you're doing good. And that is using double action not single. Remember that once you pull the hammer back for single, if you don't take the shot, you have to lower the hammer on a live round.
Someone mentioned doing work on the moving parts - I've used Wilson replacement springs, have polished the bearing surfaces of internal parts to help slick up the pull on double action, but have never touched the sear surfaces and you're asking for trouble if you do. Shooting also helps to make the action smoother.