Start with a 9 twist or faster in 223.
Get an identical second when needed in 243.
Get an identical third when needed in 270.

It is easy to find good deals on nice used guns, such as Rem700, Win70 pushfeed, or Ruger77 including tang safeties. Don't buy junk just because it is cheap.

You could go with all Ruger Americans if you want a consistent platform, but I don't think too many kids are going to have the "proud factor" going on with that level of quality. I know mine don't. They know the Americans are for throwing around and blazing away, but not one of them has asked for that to be their rifle. They all want blued/walnut for their own gun.