I started my kids off with a .270 using remingtons recoil loads. Now that they are older they don't need to use them, but they have a larger caliber gun for when they do need it. That being said, there have been a lot of .243 that have killed deer also.
I would ask these questions: How are your kids now? Boys or girls? Will they ever be hunting anything other than deer? How far of a shot will they be taking? Are your kids big/mature for there age?
Kids don't stay kids for long. Good luck in your decision.