Welcome to the Forum. From your photos it looks like you have a 38 Double Action, 2nd Model revolver. They were made from 1880 to 1884 in serial number range 4001 to 119,000. These revolvers were chambered in 38 S&W caliber. Your revolver would have shipped around 1880.
Value is relatively low on these guns. You probably noticed a star near the serial number which indicates that it was returned to the factory. Likely it was re-nickeled at the factory upon it return. The month and year it was returned should be stamped on the butt-frame under the left stock. Be careful if you have not removed the stocks before, since they have a pin holding the bottom of them in place and if you pry in the wrong direction, you can crack the base of the stocks. If I were to guess on a factory refinished 38 DA value, it would be somewhere around $200 - $250.
Currently loaded factory ammunition from Remington, Federal, Winchester, and some European companies are loaded very light and are designed to be used in any top-break 38 DA in good working order. Don't worry about the Black Powder vs Smokeless, alarms raised since the companies who design and manufacture currently available ammunition would not be selling their ammo if dangerous to use.