Are you
confident that the revolver is chambered in .44 Russian? The gun looks like a S&W double-action top-break, but it's substantially different from a S&W .44 Double Action 1st Model or .44 Double Action Frontier; the trigger is wrong and the cylinder appears too long. Also, the serial numbers of the double-action .44s never approached the 150,0xx range; IIRC they ended just under 55,000.
If it's actually chambered in .44 Russian, it's probably a European copy. Oodles of cheap knock-offs of S&W top-breaks were imported in the late 19th to early 20th century and have been misleading would-be collectors ever since.
Most came from Spain or Belgium; FWIW the "MARCAS REGISTRADAS" marking on the frame of modern S&W revolvers is intended to make the S&W trademark legally binding under Spanish law in an attempt to stop this practice. A genuine S&W top-break will have a relatively small (about dime-sized) circular S&W logo on the RH sideplate next to the grips. Check the gun carefully for other small proofmarks; certain ones are dead giveaways of European manufacture. FWIW the quality of these guns ranges from fair to abysmal, and
they are generally unsafe to fire, even when they were new.
OTOH the gun, to me, looks remarkable similar to a
.38 Double Action 3rd Model, and the serial number would be correct for a gun made ca. 1888. This gun would be chambered in .38 Smith & Wesson (.38S&W), an increasingly obscure caliber that's not stocked by most big-box sporting goods stores anymore, but is still available at specialty gun shops.
(It is not the same as .38 Special, which uses a much longer shell case that will not fit in a .38 top-break.) Based on the non-original finish on the hammer and trigger and the "dimpled" look of the finish on the frame, it looks like it has been refinished, which is common because the original nickel finish wasn't very durable. Refinishing hurts the value of antique guns like this one.
If the gun is in fact a refinished .38 DA, its value would be $175-$250 once it's functional, and I wouldn't hesitate to use it as a shooter.