Oakley persimmon is a good brownish lense for all around conditions - I dunno about your specific hill. Most people don't like polarized lenses for snowsports b/c it makes ice hard to see. I agree with that myself.
I've always been told that women should get women's ski/board equipment as it is designed for them.
Consider a used burton feather, very popular learning board for women, then flip it later once your g/f has defined her riding style/preferences with more experience.