It's a .38 Military & Police Airweight. The serial number dates it to 1953.
These became known as the model 12 when S&W began assigning model numbers ~1957.
The Airweights (aluminum frame) also had aluminum cylinders (thing that holds the 6 rounds of ammo) until 1954 so there is a good chance yours has the aluminum cylinder. If that's the case then it should not be fired. The aluminum cylinders could crack from firing so they were replaced with steel cylinders. You can check the cylinder by placing a magnet on it. If it's steel the magnet will stick. If aluminum it will not.
Value depends on condition but ranges from around $300 in good (about 75% of original finish left) to $700 in excellent (no finish wear). If the cylinder is aluminum then it is worth an additional premium. These values are based on retail. If you sell it to a gun / pawn shop you'll get about half those values.
The 3150 number is just an assembly number.