The initial post states that the young lady has a shoulder problem and thus has concerns about recoil. Given this, recommending a .308 (and definitely the .270) seems inappropriate. There aren't any deer in North America that can't be taken down with a properly placed .243.

If, for some bizarro reason, the .243 is deemed too small, then the 7mm-08 is a better choice than either the .308 or the .270 due to noticeably milder recoil.