callken:
You have a S&W .38 Military & Police Model of 1905 1st Change or 2nd Change. The 2nd change will have two pins to locate the extractor in the cylinder.
Both variants were manufactured between 1906 & 1909 in the serial range 73251 to 146899, averaging the production over those years I would guesstimate 1907 for your gun.
Safety issues:
Your gun predates heat treatment of cylinders, so don't shoot jacketed, semi jacketed, PlusP, +P or +P+ rounds through it. These may lead to a bulged cylinder. Lead standard velocity loads should be safe as long as it passes the revolver check out thread stickied in this sub-forum.
It predates the positive internal hammer block safety introduced in WWII after a fatality with a dropped gun. I would treat it as a 5 shooter, leaving the chamber under the hammer empty.
The above out of the way, it should be a fine shooter. S&Ws guns were handcrafted back then with high qualities of fit and finish.