Last year I was faced with the same question but for my daughter-in-law. There are a number of good choices in calibers; but it is more important how the rifle fits the shooter, more than the caliber.
Shooters vary in recoil tolerance. My DIL, though petite and a novice shooter; seems to tolerate recoil fairly well. But found her husband's 270 W. to be more of a challenge to shoot than his 6 mm Rem., or my Winchester XTR 257 Roberts. I had considered cutting down the stock on the 257 XTR, but decided not to.
Her rifle is a M70 Compact that with scope weighs just over 7 lbs. The shorter action, stock and barrel length fit her better than the longer action and barrel of the 257.
Because she lives in Colorado and hopes to hunt elk at some time; I chose a 7mm-08 as being more flexible than a 243.
My son and I both handload so we have her shoot 120 Nosler BT for practice and for antelope and deer, then 140 g. partitions for elk. With the 120 g. bullets the recoil is only slightly more than a 243 and she has the option of using heavier bullets for larger animals -- yet still have a rifle she can handle, carry and shoot.
That is how my son and I addressed the question. There are a number of good caliber choices (e.g. 243, 6 mm, 257, 260, 6.5X55, 7x57), but we felt choosing a 7mm-08 gave more choice in rifle makes, availability of factory ammo in a pinch and more confidence if she hunts elk.
