For woods hunting, a lower power scope with a wide field of view is best. On my two .308 rifles I have Leupold 2x7 and 1x6.75 power scopes. On the lowest power setting they have a wide field of view and are very fast to use, On longer shots, they have all the magnification I need.
Are you only hunting in woods or do you hunt some fields too? If you are hunting strickly woods do you really need a scope or can you get by with iron sights? Judging from your location I would guess it's a lot like the way we hunt in south central New York. I agree with Old Professer stay with lower power scopes. I use use a Marlin Lever 30-30 with a Leupold 2-7x33 shotgun scope on it. I find the Heavy Duplex Retical is just right for woods shooting and small open fields.
Some good advice but I say never say never. I agree 100 % with the larger objective but I would say a 3X9X42. You keep it on 3 or 4 power when the shooting is thick and close. As the woods (fields?) open up you increase your magnification. That 308 will shoot a long way and if you get that once (maybe twice) in a lifetime 300yd shot that 9 power will come in handy.
When I hunt the big woods up in the Adk mts all my rifles that are scoped max out at 9 or 10 power and when I am on watch in the morning or evening I got the power cranked righ up. Just got to remember to lower it back down whey you are walking back to camp!
What does "gauge" mean anyway? As used here gauge means the number of round lead balls the same diameter as the inside of the barrel (aka the bore) that it would take to weigh one pound. It takes 12 lead balls the same diameter as a 12 gauge barrel to weigh a pound. The smaller 20 gauge would require 20 balls of that barrel diameter. The larger bore 12 gauge would require 12 lead balls of the bore diameter to weigh one pound.
In general the number of pellets in a shotgun shell...