That's a nice looking gun.
According to my copy of the Standard Catalog of Smith & Wesson, 3rd Edition
, you have a S&W .38 Military & Police Model of 1905, 4th Change. The serial numbers for the .38 M&P 1905 4th Change run from 241704 - 1000000, being produced from 1915 - 1942. The book lists the values as:
Very Good: $250
It goes on to say that nickel plating (yours is nickel plated) is worth a premium (doesn't say how much). I'd probably put yours around $400, given its nickel plating, with finish wear, and the pearl grips.
If it times and locks-up correctly (i.e. the cylinder turns and locks into place before the hammer falls, both in cocking the hammer for single-action and in pulling the trigger through the double-action), and if there aren't any issues with the bore or the chambers, it should be safe to shoot. According to the SCSW3
, heat treating began approximately around serial number 316648, so it should be fine with any standard pressure .38 Special load. Personally I'd limit its use to lead-only bullets in light loads, or probably I wouldn't shoot it at all (maybe enough to be satisfied that it does
shoot), given its age and heirloom status; there are plenty of S&W Model 10s out there to shoot .38 Specials through (your M&P is the precursor to the Model 10).
Welcome to the forum!