".38 S&W Special & US Service Ctgs", from the markings on the left side of the barrel (right-click on the first photo, then left-click on "view image". Then left-click on the image and it will enlarge, the markings are clearly readable.
It's a Military & Police 1st Model 1905 made between 1906-1909 in .38 Special and the "US Service cartridge" also stamped on the barrel refers to the 38 Long Colt cartridge which was still used by the US Army and had been the Army standard until replaced by the .38 Special. The 38 Long Colt is the same size case as the S&W 38 Special and can be fired in that gun but it's a bit shorter and less powerful...which led to its demise.
Value could range from $200- $400 +/- but, if it's a family heirloom...priceless.
This one is a a little earlier, an M&P Model of 1902 made about 1904
Your revolver was built on the "K" size frame. It's hard to tell from the photos if it's been plated or if the blued finish is worn. If plated, carefully remove the grips and see if a large "N" is stamped on the frame. That would indicate factory nickle.
The very early M1905 hand ejectors were shipped before S&W determined that it was necessary to heat treat and harden the revolver's cylinder in the manufacturing process.
Welcome from Virginia! I agree with mrerick and several others, early Model of 1902 . She certainly has a hard-won patina. And a nice Brauer Bros. Holster. Standard velocity .38 Specials should be fine , but stay away from any of the +p loads. Hank