Wow...you have a very nice example of a German combination gun with an extra set of double gun barrels. Proofed and probably made in Suhl, Thuringia and retailed by L. Damm Barmen who is quite possibly not the maker. Made "for the trade" meaning Barmen possibly ordered it from a maker in Suhl. Witten Excelsior is the steel from which the barrels are made, good stuff. 16 is the bore and the circled 16 indicates 2 1/2 in. chambers rather than the more modern 2 3/4 and the W on the left barrel simply indicates that it was choked but it's never mentioned what the choke is. 2 1/2 in. ammo is available from RST and others.
The right barrel of the set that is a rifle appears to be for the 9.3 X 72R Deutsche cartridge, a very popular cartridge of the era for combination guns and drillings. Sellier & Belloit still make ammunition for it that may fit and as the rifle is Nitro proofed it should be safe to fire but should be checked by a gunsmith competent in old German firearms. I can't quite make out the stamps on the side of the rifle barrel but that is the bullet weight and type for which the rifle was proofed. In 9.3 X 72R it is generally a bullet of about 200 grs. weight and in your case was a steel bullet. The combination gun barrels have the typical for the era claw type scope mounts. It also has the Greener crossbolt, that extension with the hole in it that extends from the rear of the barrels and the corresponding bolt in the top of the receiver. It also has the side clips, those extensions on the sides of the bosses. Very strong.
As there is no date code stamped, that I can see, I'm fairly certain that puts it pre-1921. Yours is somewhat rare in that it has two sets of barrels. All that is left to complete the ensemble is the claw rings and a period scope to go in them. The rings can be made but unfortunately they are pricey. The gun is a fine example of German craftsmanship of the era and, even today. You didn't mention it so my hope is that you are not thinking of having it re-finished. Please don't. If you do you will remove approximately 1/2 the value and the world will suffer the loss of yet another fine, original German firearm. I'm certain you're quite proud to own it, you should be. First of all for the men it came from, your Dad and Grandfather, and secondly for what it is. Again....Wow!!! Very nice!!!!! Congrats!!!