Re: Remington Derringer
That is the one called the Type II or Model 3 double derringer. The 984 is not really a serial number as the numbers were repeated over and over on those guns; it might better be described as a batch number.
Now the bad news. The left side receiver "ear" is broken off, and the right side one appears to be cracked. That gun should not be fired at all.
Further, the gun has been heavily buffed, then "reblued" in a way that has resulted in the iron frame taking on a reddish cast which is not an original color. So the gun has about zero collectors value, and I hope you have not a lot in it.
There is no way of choosing which barrel fires first; every time the hammer is cocked, the barrel selector moves a notch, up or down, so which barrel fires is whichever didn't fire last.