7mm-08, (7x57) 260Rem, (6.5x55) stick to these calibers. My wife shoots a 270Win, and even moderate 130gr. loads were too much for her, we had to settle on 100gr. Barnes X's(now discontinued, but we stocked up).
Suggestions like 30'06, or 7mm Rem Mags for a newbie and a lady too boot is very short sighted. What a perfect way to ruin a begineer, get them a rifle thet is far and above more recoil than a lot of full grown men have trouble with. Remember women are most likely not macho types.
I bought my kids a 7mm-08 NEF single shot in the youth configuration, my 10yr. old Daughter (lefty) has no problem with 120gr. handloads doing 2600fps, she laugh because it's so loud. My son (7)(righty) will shoot it but even with the 12.5" LOP hes a bit overstocked, but he's a mans man, he likes the shooting even if his form suffers. BTW the rifle cost a pitance at $350.00, and stocks can be had for $35.00USD.
Find some friends who's wives shoot or contact the membership of a local range and see if your lady can test drive a few calibers, that way it's her choice to make. And yes all the calibers I mentioned can take on stuff bigger than deer, it will just require getting a bit closer, and picking the shot. Wait a minute, we probably all could follow that advice.
Good Luck.