Do the 243 then get the 270 later. Easy to find a smaller framed 243 that she will be more comfertable with. If she stays with it get her a nicer 270 later or semi auto -06 if she happens to get the Elk bug. Don't want her flinching while she is learning to shoot. .22 are way under rated for kids on many levels. My kids can put a couple of hundred bucks of ammo into dirt hill so fast it will make your head spin. Thank god for the 22s when they get bored with em they are bagging for the bigger guns.
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When Ma Nature decides to make ya her bitch, aint nothin your gonna do about it