If the largest game she'll hunt is deer, I think I'd have to recommend the .243 as well. I've been using it since 1978 in spite of now also having a number of other calibers to choose from. It's been very adaptable to range sessions, prairie dog shoots, coyotes, pronghorn, and deer. Although I've taken 3 elk with it, I would probably recommend the 7mm-08 if elk are going to be on her menu.
The BEST way to find a rifle that fits her is to take her along. She sounds like she may be smaller-statured, so a "youth" model might be a good place to start. However, that's not a guarantee. Take the time while you have it to do it right, let her be actively involved in the selection. I would even offer that caliber is going to be less a factor in her comfort than proper length-of-pull, manageable carry weight and overall length.