There's only one real choice for somebody who doesn't handload, the .243 Winchester. It's not only great for beginners but many veterans choose it as well.
My wife started hunting in her 30's with my grandmother's old .257 Roberts, but it was a little heavy. Since then she's hunted big game all over the U.S., as well as in Canada, Europe, New Zealand and Africa, with rifles chambered for over around 10 cartridges up to the .30-06. But recently she's become more sensitive to recoil, and last year picked up a light Hiusquvarna .243 that's now her favorite general-purpose rifle. It works on deer and antelope as well as anything she's tried, and a couple days ago she took her 100th big game animal with it, a pronghorn at 243 yards!
