Condolences on your loss.
That is a M-1905 Military & Police, 3rd Change, made between 1909 and 1915. (I looked up the serial number in my Standard Catalog of Smith & Wesson). If that hasn't been refinished it is in exceptional shape for its age. As mentioned by someone above, the grips are aftermarket.
Assuming that the timing and lockup are good, it's safe to shoot with standard pressure .38 Special ammunition. Note that while it's made from steel, S&W did not heat treat the revolvers until about 1919. It should shoot close to point of aim with 158 grain standard pressure loads.
Do not shoot any +P ammunition in it. It is unlikely to blow up but will greatly accellerate wear and tear.