cinmoon1: Your gun is almost certainly a .38 Military & Police, the model that eventually morphed into the Model 10 when S&W started assigning model numbers in 1957. Based on the serial number, it dates from the 1915 (SN 241704) to 1942 (SN 700000) period - you can interpolate using that information to get an approximate year of production, but it would only be an approximation.
Assuming no unusual mechanical problems, your gun is safe to shoot with any standard .38 Special ammunition. The SN indicates that it dates from slightly after when heat treating of cylinders was introduced, which is often interpreted to mean that it would also be safe with .38 Special +P, but I would not recommend subjecting such a nice old revolver to the hotter loads.