Took my little sweetie on her first hunt a couple of years ago. We're heading-back up to the Kiabab this weekend again! We always have a great time on that doe hunt with the kids..... ;-)
No doubt, that hunting with your kids is the best! She was shooting a Remington 7400 .308 caliber. I picked the gun up cheap while in college many years ago. Turns-out it's a great gun for the kids, as the semi-auto action helps greatly in reducing the recoil. Kind of like a built-in shock absorber!;-)
When the kids are young, I usually have them use it as a 'single shot' for safety reasons.
All three of my kids have killed their first animal or two with it, and she'll be packing it again next weekend!