There are some good choices here and all of them will work for deer sized game and if you make the right choice for that ocassional elk if that's in the cards. Most women love the .243, .260, .7mm/08, .308 and the .25/06 and all of them are light recoiling, with good accuracy using light bullets. Now that Remington has reduced loads in a variety of calibers that opens up many other options. Just make sure you start with a shorter length of pull that fits her, and a good recoil pad like a decelerator or Simms etc, in any caliber. There are some excellent womans/youth models out there from some quality companies for you to choose from that come set up with this in mind. Make it fun for them and they'll enjoy it more and want to shoot with you. Just don't make the classic mistake of trying to think you know just how much recoil they like (everybody's different) and over gun them and you'll be fine.