probably a model 17 or 18. look in the cylinder frame area for model number
I frame
On the frame and the grip frame.
Caliber can not be idenitifed by sn. Take it to a gunsmith if it isn't marked on the frame or barrel.
You will need to check egunparts.com
K
It had two different caliber barrels on the same frame.
The Iver Johnson Trailsman model 66 large frame revolver was made from 1958-1978.
You will need to check egunparts.com
L frame, blue steel revolver in 357 Magnum
On the frame
Assuming it is .38 caliber and therefore a J-frame, and without knowing condition, $150-$300
If you call S&W they will tell you when it left the factory.