Welcome to the Forum. These are great guns to own, but values have barely held their own for quite a few years with some drop in demand by collectors.
Most all S&Ws are dated by the date they left the factory and not manufacture dates, but some manufacturing log books remain in a private collectors hands. The standard dates given are ship dates and if you get historical letters on those guns, they will show that date.
The S&W 44 Double Action chambered in 44 Russian were manufactured from 1881 to 1913 in serial number range 1 - 54,688. That revolver would have likely shipped in 1888-1889 time-frame. The 44 DA Frontier was chambered in 44-40, but your revolver is not a Frontier Model since the serial numbers only went to 15,340.
The S&W 44 New Model 3, chambered in some 10 to 15 calibers, was manufactured from 1878 to 1912 in serial number range 1 - 35,796. Your revolver would have shipped somewhere around 1880. You may get other guesses, but this model was serialized in very large lots and then sold off without regard to sn# order. In the database, a 67XX shipped in 1882, while a 91XX example shipped in 1879. There were no 1877 named New Model 3s, but there was a Colt Model 1877.
All this means that if you want some history about the guns and where they shipped to and when they shipped, you need a factory historical letter. The cost of the letter is $100 and applications can be found in the S&W Historical Foundation link.
