Oh, I see Carguychris is back and helped the next one.
- your gun is an older, 1963 model. Should have diamond-centered "magna" grips on it, kinda like the ones pictured on the M&P below. Should also have the S/N inside the right grip panel. It was introduced in 1955 as the "357 Combat Magnum" and became the "Model 19" in 1957. In 1970, a Stainless model was made, called the "Model 66."
A picture would be interesting if you have one - these old magnums are great. The 4" was the standard length for most of it's run. There were a few 6" and longer ones later, as well as 2.5", too (I have two of those).
Major note about these is to not shoot hyper-velocity "light" magnum loads - 125gr. or 110gr., etc. Don't shoot magnums less than 158gr, or it can create flame cutting on the top strap and possibly crack the forcing cone of the barrel. These loads came later, and the design of the gun isn't up to those loads. Because of this, in 1980 S&W introduced the model 586/686 - slightly beefier cylinder and yoke/barrel area. The 19/66 was discontinued in the late 90s, I believe.