I started my youngest son with a .243 when he was 12 or 13 and plan on using the same rifle this year with my 15 year old daughter since she's expressed an interest in going hunting for the first time this year.
The .243 is a great round. I use Remington Core-Lokt in 100 grain and trust them implicitly. But hey . . . that's just my opinion. There are plenty of great rounds out there in .243.