Welcome to the forum.
Does it read Smith and Wesson with an address and patent dates on top of the barrel (you'll need magnification)?
If so, you have a ".38 Double Action Safety Hammerless 2nd Model" made approximately 1887. It is a Top Break with 3 1/4" barrel. Yours appears to be nickel plated in the photo and is common. It is chambered to shoot the .38 S&W Cartridge (not .38 Special) still available today.
The original correct type grips are Gutta Percha black hard rubber with the S&W monograms at the top and checkered surfaces:
Later walnut grips were available on the Hand Ejector I frames any of which will fit your gun all the way up to 1953 and can easily be found on ebay and Gunbroker. They look like these: