To really get the most out of drilling, you need a good rifle caliber and a removable telescopic sight. It is fairly easy to find a 8x57R or 7x57R in shootable condition with claw bases on the barrels. German hunters would store their guns with the telescopic sights in an individual carrier, and GIs had a habbit of missing them when they "liberated" the guns during WWII. Also why I am sure there are far more quality pre-war drillings in this country than there are in Germany. The vast majority of these guns will be 16's.
J.J. Perodeau at Champlin Arms can make you a set of rings to fit those bases in 1" or 30mm. The little straight tubed Vari-X II or III leupold works great in them. You can also find a gun with a period german glass attached that is still in shootable condition. Modern guns with a modern scope bring a really big premium.
None of this is really cheap of course. But you can likely find a solid 16x16x8x57R in nice shape with claw bases for 2500 or so. JJ will charge you something over $600 for the rings and the scope will be whatever you decide to invest. You could have great combination gun in a very useful caliber with excellent glass for under $3500. Not too bad.