referring to this round as a pistol
i've used it to put down boar at under 50 meters whereas before i would stick to .44 magnum or 1oz foster slugs. 300 blk has the benefit of a familiar platform, easier suppression in my particular use-case, and higher magazine capacity while being in a carbine-sized package.
i would imagine it would do well in personal defense scenarios and have done shoot house with an MCX that gives me confidence it can put down men with authority and in a controlled fashion. i view it similarly to .30 carbine: a transitional cartridge that can be a pistol or rifle round but is designed for rifle (or carbine) use. it would probably lose a lot of value in a traditional rifle or pistol, but works best in a carbine/SMG type role.
I want a 12 ga. pump. She wants a .22. I think she is afraid of larger calibers (she's only 5'1")
while .22's are fun, there can be issues of reliability and sheer energy (or "stopping power") where you will be much more dependent on shot placement for effectiveness. while for the uninitiated a shotgun is intimidating, light target loads can be used (and 20 ga might be significantly more expensive and harder to get depending where you live) to get used to the action.
assuming you're mostly using this for defense than hunting, you have to ensure that she has confidence in the weapon, is able to work the action with authority to avoid short-shucking the action, and to get over the intimidation factor of a large (for a petite/short woman) weapon. consider the Maverick 88 in 12 gauge and use recoil control loads (start off with #8 target/dove loads or #4 buck with recoil control).
for a purely in-the-home shotgun, full power 2-3/4 is probably overkill in most situations.
1. #8 target is light and cheap to shoot and builds confidence while being useful for pheasant and smaller game like grouse. target loads are also light recoiling and still lethal, although with fairly poor penetration.
2. #4 buck is decent for the smaller side of medium upland like wild turkey if you use an improved modified choke or want to use it as a defense tool. #4 is often used for law enforcement shotguns for this reason since it's lethal enough yet controllable even for smaller officers and can be used reliably in most gas-operated shotguns, recoil-operated, and of course manual actions (slide, bolt, et c). around 1300 feet/second is appropriate for #4 buck.
"recoil control" basically means a lighter powder charge and comes with a "power piston" or spacer most of the time and has a couple tradenames (Federal "FliteControl" for example).
enough, we'll never get to see it jingled out to its full potential by some ANA boot. 
