What you have is a five-screw K-38 Masterpiece. Compared with a newer three-screw gun, it has an extra screw on top of the sideplate and another one in front of the trigger guard that retains the cylinder stop plunger spring.
When S&W introduced model numbers in 1957, it became the Model 14. The top sideplate screw was omitted circa 1955 and the cylinder stop screw was omitted circa 1961. The "fish hook" hammer is often found in early postwar guns.
I would estimate the value at around $700. With original grips, it would be worth more.