The question of gun recommendations for wife/child always brings a lot of opinions and suggestions. The 243 is frequently suggested. Persoanlly, I'd suggest a 260 Rem, 7-08, 308 Win, 270 Win or 30-06. Depending on her stature, you may want to look at a youth rifle. Be sure the gun/stock fits HER. When shooting at the range, insist on her using both the foam ear plugs and ear muffs. Consider using a "sissy pad" (small sand bag between shoulder and recoil pad) at the range. Be sure the gun has a nice recoil pad (Limbsaver or Kick Eez are two than come to mind).
If the bullet weights and velocities are the same, a 270 and 30-06 will always generate more recoil than a 260, 7-08 or 308 because they require more powder. The elements in calculating recoil are bullet weight, powder charge, muzzle velocity and gun weight. Here's a Recoil calculator
if you want to play around w/ the #'s.
As far as which caliber to get, it's mainly a matter of personal preference. OTOH, I would strongly recommend on using "Reduced Recoil" loads w/ whichever gun you decide on. Nothing wrong w/ the 30-30 for deer hunting, but it will limit her some w/ distant shots. If she's going to hunt inside 200 yards, the 30-30 is a fine gun.