I started shooting when I was 5 years old. As far as youth bows, here are a couple recomendations. I know kids who start out shooting at the age of 4.
To be honest with you, it is not only my opinion but many of the top level coaches all agree, that young kids should be started out on a smaller recurve bow, shooting fingers. This will teach them better eticate and form then jumpin right into a compound with a release. This is also a way to find out if the kid is interested without spending a few hundred for something that is going to last them. Recurves have no draw length per say so it will fit them, as oposded to the cheap compounds that dont have any adjustment. A recurve also builds muscles faster. You can get a nice recurve for youth for under 100 bucks.
PSE Chaos - Fastest low poundage bow on the market, MSRP 359.99, comes with Whisker Bisket, site, quiver and arrows. This bow has been the buzz in the industry this year. It has a draw length adjustment. Available in poundages from 15-30, 25-40, 35-50, and limbswap is about 60 bucks.
Darton Ranger 3 - This bow has the widest range of adjustment. The draw weight is adjustable from 15 - 45 and the length from like 13 - 27. This bow has an amazing wall and great letoff, I think it runs about 239.99 for just the bow.
If the kid wants to shoot let them! Its a great sport and it gets the away from the video games!
If you do some research and have some questions, send me a PM, I have been shooting for 17 years, 15 years competitivly, I love to help people get into archery.