Everything BareBack Jack mentions is perfect for a woman who wishes to hunt everything up to and including elk and moose.

I personally would lean toward the .260 Rem or the 7mm-08 Rem, but the .270 Win, .280 Rem or .308 Win will be fine, although they will kick a bit more. The little Browning A-bolt Micro Hunter in .260 Rem would be a perfect rig, I would think. And so would Briman' s Model 7 in .260 Rem or Winchester' s Model 70 Classic Compact in 6.5x55mm Swedish (if it comes that way) or 7mm-08..