If deer are the largest animal hunted there is really no reason not to choose a 243. Not just for a girl, but for anybody. Conventional wisdom has always said that a 243 was borderline, but in 2013 with the better bullets available that is no longer true. A 243 is just about the perfect deer round for anybody today. You can use larger if you want, but you don't need to.
If you think larger game may be in the future a 7-08 would be the next step up and the smallest round I'd use on all other NA game.
Nothing wrong with a 270, but you are starting to get into more recoil than some smaller, less experienced shooters want.