For deer with a new recoil shy hunter you just cant go wrong with a 243 for less than 450 yrds with the right loads. For elk you would be looking at a different caliber. Not that a 243 cant do it because thousands have died from a 243 but with a new hunter I would opt for something with a little more horse power. I would give the 7-08, 260 a try if she is really little. If shes a bigger frame gall then I would try maybe one of the short mags. Either the remington or winchester short mag would do, but I would go with the winchester because it is more popular. If it is to much then have a muzzle brake
put on. As for the short mags I would think any thing from the 270 to the 325 would work just fine. My favorite would be either the 7mm, 300 or 325. My little brother got a 300wsm for his 12 birthday and he handles it just fine. Course My familly is a little bigger than normal since my 12 year old brother stands six foot and 200lbs wearing a size 14 shoe. My dad and I both started out with 300wins and decided my little brothers first rifle should be close to the same. Hope this helps. As for rifle I have always had good luck with remingtons or savages.