Yeah, the 357 is the way to go. Corbon offers a 180 grain 357 Magnum loading that won't beat the snot out of her. Most likely, the chamber will accept factory 360 DW ammo (a premium loading offered by Dan Wesson) I don't know if DW offers factory loaded 357 Maximum ammo, but if you reload or know a reloader even full house 180-200 grian loads in the 357 Maximum are quite user friendly.
I plan on using my 357 to introduce my grandsons to shooting, but I've a few years yet to wait (Oldest is 3 at present)
The 44 can be equally user friendly, CCI Blazer ammo is cheap enough and mid range powered. It was some of the first ammo I ran through my 44 and while I never got a shot off with it at game, I've no doubt it would do the job. But full house loadings in the 44 are not the most user friendly, in fact I prefer 30-30 to fullhouse 44 cal 240 grainers. The heavies...270-300 grains are more user friendly but do require reloading.
The 243 is a nice rifle....for an adult. It has lots of muzzle blast and lots of muzzle rise which can be disquiteing to a young shooter....my daughter never took to it, my wife liked it well enough, but wouldn't hunt after making a less than perfect shot once. The animal was recovered but her ideas/ideals about killing game and all about how it's supposed to go never did. I'd argue for the 30-30 over a 243 especially if hog is on the schedule