jd32:
If the patent stamping into the timber of the grip, the cylinder swings out to the side and has six chambers, then you should have a .32 Regulation Police manufactured sometime between 1920 & 1929. The barrel should be stamped .32 Long CTG on the right side and Smith & Wesson on the left.
If the cylinder tilts up and has five shots and the gun has an external hammer, then it is a .32 Double Action 5th Model manufactured between 1909 & 1915. The grips are probably not original to that gun.
.32 S&W Long is still available, as it .32 S&W (which is a shorter cartridge - don't buy longs if your gun is the five shot version). Old Western Scrounger is a good source:
http://www.ows-ammo.com/store/
Neither gun has a modern internal hammer block safety, so leave the chamber under the hammer empty. Otherwise if dropped they could fire. Both guns should be safe to fire with modern factory ammo if they are mechanically sound, neither should be fed any sort of 'hot' handload. The .32 Double Action is chambered for a round that was originally black powder, modern smokeless powders have faster pressure peaks, putting extra strain on the gun. It also pre-dates heat treatment of cylinders, so don't stress it.
If your gun doesn't match the above data then we will need photos of both sides of the gun to try and determine what you have. There were many cheap handguns chambered for the .32 S&W or .32 S&W long that were not S&W products.