Both of my kids are left-eye dominant which makes them lefty shooters. When they got bored with the chipmunk .22, they both got into pistols over rifles. When they do shoot long guns, they prefer the single-shots (Contender/Encore) or '92 lever actions, which you can get in some good woods range hunting calibers. I went the route of ambidextrous actions so everyone in the family can shoot everything in the armory ... if they wanted to. My 17yo daughter is also a good shot, but does not enjoy large calibers or hunting, so I've found she prefers the .38/.357 lever guns and handguns (.22, .32, .38/.357, .380, .40). She tried .44 once just to get a feel, but not since.
Edit: Just thought you might try looking at Handi Rifles too. Inexpensive, well made, accurate and good caliber selection, and if they don't like it, you can more likely sell it or rebarrel it to something to suit you.