Muddy22,
Your drilling is chambered for 8x57IR,as indicated by the 7.8mm over 57 and the proof for a steel jacketed bullet(Stmg) of 15grams weight.
The barrels are made of Krupp barrel steel. It is nitro proofed, and the crown G shows it was proofed for a single projectile(bullet)The crown U shows it went through a View proof, which is a detailed inspection, including verification of dimensions, after definitive proof. The 16 in a circle means it has a 65mm(21/2-2 9/16")16 ga.chamber. This was the standard at the time and is shorter than the current standard of 70mm( 2 3/4"). The 16/1 is the bore diameter of the barrel, ahead of the chamber. This is about 16.99mm, expressed in gauge measurement. The crown W means the barrel is choked, but the amount of constriction is not shown. The WK by the serial number(1789) is the mark of the rifle barrel maker. There were several that might have WK as initials. I didn't see a crown S, it means it was proofed for shot, if you find one. It was proofed in Suhl, but I didn't see a date( Normally found by the 7.8/57). If there isn't one the gun was likely proofed between 1911 and 1922. It has interrupting sears and cocking indicators. While incomplete, I hope you find this helpful. BTW, I think the drilling is very nice, with better than the standard game scene engraving, and I think you should keep it or pass it down.
Mike