The "Y" number in the open cylinder crane are assembly numbers,,,
The Serial number is what is on the butt of the grips.
You seem to have a S&W M&P (Military and Police) chambered for .38 Special cartridges.
After 1957 S&W started using Model numbers for their guns,,,
The M&P became the Model 10 at that time.
There are several different iterations of your gun,,,
I'm not expert enough to detail those for you.
Suffice it to say you have a vintage handgun that should shoot modern ammo just fine,,,
Avoid shooting any .38 Special ammo labeled "+P" in your gun,,,
Regular .38 special ammo should be just fine.
I hope that helps,,,
Caje: The coward dies a thousand times, the brave only once.
Kirby: That's about all it takes, ain't it?
Combat: "A Silent Cry"
Aarond is good,,, Aarond is wise,,, Always trust Aarond! (most of the time)