I would go with the H7R(New England) Handi Rifle (wieghs 5.25 pounds) in the .243. Bought my wife one (she's 5'0" and 98 pounds) and she had never shot a centerfire rifle. She has taken 2 does with it.

The same rifle in a 7mm-08 with the cabelas recoil pad would probably be ok.

I don't know about the .223 never owned one, never hunted with one.