Thought I'd purchased my ideal drilling a few years ago, a Sauer 12x12/.30-06 with a 6x32 Zeiss scope. It seemed like the perfect all-around/travel gun, and I was doing more traveling then, since ammo for each could be found anywhere. I even shot it very well as a shotgun: After getting used to the swing, broke 25 straight at trap in my second round.
But eventually decided it was too heavy as a scoped .30-06 and not quite right when unscoped as as 12 either. My favorite drilling now is a 16x16/6.5x57R purchased from luv2safari. It's light enough to be a lively 16-gauge without the 4x Hensoldt scope, and the 6.5x57R is plenty for anything I plan to hunt with a drilling here in Montana--which is my major, realistic use for a drilling anymore.
My other drilling is a century-old hammer Sauer-Daly back-action sidelock in 12x12/.30-30. It's pretty useful too, partly because it has a flip-up tang aperture sight. Have taken both big game and birds with both--and like 'em both.
My point, I guess, is that any shotgun gauge from 20 to 12, and any basic big game round will do the job. Admittedly I like to keep things simpler than some other hunters might....
