A .260 sounds like a nice choice; however, I guess it depends on the woman. About 5 years ago, I bought my wife (who had never fired a gun of any kind) a Ruger .243 lightweight (now "Hawkeye"). She finally got around to trying it out last March, after we joined a club with a good range. On her first outing, I had her shooting from a rest. We worked on breathing and trigger. She finished the day with a 5-shot group at 100 yds., max spread 1-3/8". But she heard me sighting in my .270 (also a Ruger M77 Mk II), and said, "I want to shoot that rifle!"
The .270 was working 150gr. SP with 53gr. of IMR4350, which it really likes. SO the next weekend, I let her shoot it. She instantly fell in love with the 270, in spite of its "bark" and "bite." We will go out next Saturday for the Opening Day of our whitetail rifle season, and she'll get a chance to carry her .243 around all day. -Shooting is one thing, but carrying a rifle around all day is something else. My wife is a weightlifter, and in good shape at age 29, so it should be OK - but maybe the .270 would be a little much.
We men tend to have more forearm strength than women; that's an evolutionary thing. But my point is, that carrying a rifle is as important as the recoil. Deerhunters do a LOT more carrying than shooting! How heavy, and how long is this .260? That's also a factor in the decision.