Here’s my $.02, my daughter is an average to smallish 12 year old. I started her with a 223 at 8 yo. She shot that 2 years before I decided to get her a left handed rifle instead of shooting my right handed rifle. I went with a 243 for the new rifle. If I were doing it again I would have stayed with 223. I do not hand load, so that could make a difference. Your 13 yo can probably handle the 243 or 6.5, but the 243 recoil is all my daughter wants. It’s not an issue shooting deer, but it is shooting paper for practice. Of your three choices I vote fast twist 22-250, especially for the younger kids.