See pic for location of serial number. You'll have to remove the grips too see it. There will be a letter prefix such as "S". If the SN is S761xx then it dates to 1950 and would be a model 357 as that was the only model in that caliber that S&W made back then. It would later become the model 27 when S&W began assigning model numbers ~1957.
The gun has been refinished. It's original finish would have been blued or nickel.