If you have the money you could get just about any combination of calibres. What is your budget?
If you are looking for a drilling on the used market then 7x57R under a pair of 16 ga barrels is probably the most common. It is a good combination too, and there really isn't any difference I could see in killing power between the 7x57R and .308 on game up to hefty pigs and deer (I've never hunted bears though). 16/16/8x57JR or 8x57JRS is also a combination you'll see. Other calibres and gauges are rather less common.
If you want lightweight and handy, look for a drilling with a Dural frame, rather than steel. This saves a fair bit of weight. My drilling is a Krieghoff "Waldschutz" model, with Dural frame and 22" barrels, and it is 6 lbs bare. I also have a 1.5-6x scope set up on claw mounts, which I think is ideal, and works well even for flushed birds when set on 1.5x.
Left handed function is not usually an issue, as far as controls go, but you'd probably want a gun stocked for left hand use. A gun for a righthander will not only have the cheekpiece on the wrong side but also may well be cast off to suit a righthander, which might affect how it points and kicks when shot left handed.
HTH
