You have a 1st Model PREMIER 2nd Variation - variation ID from the assortment of PATENT dates on the barrel rib, with an 'O' prefix to the serial number it was made between 1898 and 1900, therefore it is BLACK POWDER capable only, as defined by H&R ARMS Co.
The serial is around the middle range of the examples I've seen, so figure the year of manufacture at around 1899. It appears to have a 4" barrel which is non-standard and adds some value to a collector.
The ammo in the box is from a much later date and contains smokeless/Nitro powder charges. Occasional shooting of these cartridges may or may not cause damage to your gun - but a steady diet will most likely begin to stretch the frame and weaken the barrel to frame lock-up.
It is a nice heritage item - IMHO, retire it and enjoy the family history this gun represents.