I started my youngest son with a .243 when he was 12 or 13 and plan on using the same rifle this year with my 15 year old daughter since she's expressed an interest in going hunting for the first time this year.
The .243 is a great round. I use Remington Core-Lokt in 100 grain and trust them implicitly. But hey . . . that's just my opinion. There are plenty of great rounds out there in .243.
I started out with a regular sized 20 gauge. It puts the deer down that's for sure. And if you're worried about recoil then just remember that you wont feel a thing when you shoot at a deer, but make sure that you are able to control it well.
the 243 is a good round but if she dont seem to mind the kick of a 20 ga than she wont mind the kick of a .270. she can use the 130gr bullets for deer and, unlike the 243 she can hunt bigger game if she ever wants to just by bumping it up to a 150 gr bullet.