Re: .243 or 7mm-08??
243 was my first rifle, I still have it 30yrs later, so obviously I'm pretty partial to and started both my kids with it. I got my daughter a 7mm-08 3yrs ago at 13 she fell in love with it. I'm pretty impressed with it myself. Honestly they both kill very well, if you think there might be chance she'll go after elk some day 7mm-08 for more appropriate bullet selection, otherwise flip a coin and choose heads you'll be tickled with either. or take her shopping and let her choose the rifle she likes chambered in either cal.
Keep in mind the animals we shoot for food and display are not bullet proof. Contrary to popular belief, they bleed and die just like they did a hundred years ago. Being competent with a given rifle is far more important than impressive ballistics and poor shootability. High velocity misses never put a steak in the freezer.