6 ARC? 224 Valkyrie? …..??? For kids hunting AR?

Neither of those you have mentioned have sufficient amounts of ammo available. Go 6.8 spc or 6.5 grendel. My oldest daughter killed everything with a 6.8 for years including 4 elk. It has more power within 300 yards than any you mentioned and/or the grendel. Ammo is surprisingly more available than 6.5 grendel.
That's pretty impressive for that 6.8spc. Oddly enough you're not the first person saying they can't get enough 6 ARC ammo. At least here in AZ it's all over the place. Plus I reload so I've already procured those components. Thanks to a very generous member here the build on the 6 ARC has started. I'm sure it doesn't have the energy of the 6.8 or 6.5 but it's plenty for a 90lb-100lb coues deer. she shoots very regularly at 300 yards and that will be the limit provided she can shoot prone which here in the desert isn't usually a problem. And you're not wrong about getting them close as possible. Shots on coues deer just tend to be longer. When we hunt in TX those shots will be shorter.
 
Harvested a 20 inch 6 ARC from a 6 BRA PRS take off barrel. Buddy gave me 3. The 6 ARC sports the same contour as our AR15 competition service rifles.

Here is a picture for comparison how a donor barrel looks like. The 7.5T KBI 6 ARC is going to a young lady in AZ.

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Neither of those you have mentioned have sufficient amounts of ammo available. Go 6.8 spc or 6.5 grendel. My oldest daughter killed everything with a 6.8 for years including 4 elk. It has more power within 300 yards than any you mentioned and/or the grendel. Ammo is surprisingly more available than
I second 6.8 spc. Ammo is easy to find and deer don't stand a chance against it. If you don't go with an AR platform then my vote is 25-06
 
Thanks to @bamban we parted together her rifle over the holidays. It turned out great. The 20" 6ARC barrel will put three under an inch with factory 103 eldx. Getting 2710 fps with the factory ammo. Haven't started reloading for it yet since I'll be using the factory brass. But I've got a box of 70gr hammer hunters from a 10 twist .243 Winchester barrel that I used to have that might get loaded up.
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6.5 Grendel is better than anything you propose, it may be the best no recoil round ever produced, I have taken many species with it and its almost always bang flop. No recoil at all, if you have a good rest you will see every impact clearly. The factory rounds in 123 grain and 125 are almost as accurate as the handloads. It may be the best cartridge rifle combination I have ever owned.
 
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