RE: Browning
I know the short track is a good shooter for a semi auto. I would be kind of leary about having a WSM in an auto, they are awfully short/fat/steep shouldered cases that were prone to not feeding right in bolt guns in the beginning. Don't know any firsthand reports of them in autos (other than ARs).
I'd get the 308, it will work well out to 300 yards and beyond. Second choice would be the 300 Win or 7mm Mag.