the .243 is probably the best choice to start a youth hunter with.
the .243 has a long history of taking deer.
All I would suggest is taking both of your girls out and let them watch you take the first 2 or 3 shots,
that way they will hear what the .243 sounds like (so no flinching when they shoot)
that will also show them what sort of kick it offers. (If any)
It sounds like you're looking at the New England Firearms Superlight Youth Handi Rifle .243 Winchester, is it? is it the synthetic or walnut stock?
The NEF is a great starter rifle.
Good Luck to you and both girls, and Welcome to the site...
Democracy is two wolves and a lamb voting on what to have for lunch.
Liberty is a well-armed lamb contesting the outcome of the vote.