fastrig,
everyone else gave you their 2cents, here is mine.
270 winchester. a nice combination of flat shooting, versatility AND pretty tolerable recoil.
the 7mm/08, 7x57, 30-06 or 308 are all good cartridges, not quite as flat shooting.
shooting a 270 can be done with reduced factory available loads as well.
i don't own one, don't need one but i have recommended them to friends for a first rifle (men and women). if you need more gun later, pretty easy by then to know how much bigger to go and the 270 will take care of lots of pretty sizable game.
take her with you when you buy it and make sure it fits her and has a good recoil pad.
my 2 cents