Dave- why do you feel that she does not need on in the first place?
.
Sir, that's not what I said. Here are a couple of my key sentences:
The FIRST thing a gun has to do is, be carried by the person who's taking it.
This might be asking too much for someone not all that interested in guns. (and who probably doesn't even see the need to have her own in the first place.)
If she doesn't want to carry one, then all of this is for naught. If she's like many women, they don't feel that THEY need to carry one......you have YOURS, after all.........

Trying to make her understand that things may not go as planned might be impossible.
I didn't say there WASN'T a need, only that she may not be able, or willing, to see it.
This all comes down to the woman in question. DOES she see a need or not? Does she already shoot or not? If so, does she already have a preference? If so, then why not go with that?
If she does not shoot (much or at all) but is willing to learn, that's another can of worms entirely. If you want a chance at succeeding in this, you need to keep one principle first and foremost: Keep it fun! (for HER, not necessarily for you!)
A very big part of keeping it fun is to keep it simple. Handing her a multi-caliber folding/breakdown long gun with 6 kinds of ammo is going to get you either a blank look or the dreaded "are you really THAT stupid?" look we've all seen too many times.
Based on the foregoing, if you want more than a .22 (which is better than nothing, but not ideal) then I'd suggest a Marlin lever action in .357 magnum. Pick your ammo well and she will have fun and be able to survive any likely circumstance. Plus, it has the innocuous "Old West" look which works in your favor.
I'd suggest maybe two loads: full power .357 magnum soft points for bear (or whatever) and some .38 jacketed roundnose for small game. These are easy to tell apart and would fulfill their role as intended. The ammo is still compact and even the full power loads wouldn't kick enough in that gun to ruin the "fun factor" of it all. And those 130 grain FMJ .38's would kick like a .22.........buy extra boxes of that one.
Keep us posted !!
.