Re: .243 or 7mm-08?
My dad and I both have .243's and he has a 7-08 as well. I don't think either one is a bad choice. Both will reliably harvest deer and neither has significant recoil and can be easily handled by youth hunters.
That being said, in my experience, we get more bang/flops with my dad's 7-08. He shoots 162 grain hornady interlocks at 2550 fps. I have never seen a deer take a step from that load. Sure you can get bang/flops from a .243 as well.
Either one you choose won't be wrong. If it were me, I'd go 7-08 and work up to full loads as she gets older. Even with full loads, it isn't bad. She may be able to handle them now.