I have three kids between 7 and 12 that all started shooting when they were about 6. In my opinion the biggest concern in the very beginning is the actual weight of the bow because they just can't hold up very much weight until they build that strength up. If the bow is too heavy for them they can't shoot it for long, or will start compensating with bad form (high shoulder on bow arm, etc...). You want it to be comfortable so they can enjoy it and ultimately build the strength by sticking with the sport.
I started my kids on mini-genesis and genesis bows, just letting them plink on foam zombie targets and stuff. Teach them fundamentals of archery without worrying about aiming and scoring and all that. My oldest actually won his state tournament in NASP with the Genesis the first year he competed because he already had about 4-5 years of practice on fundamentals. Learning to shoot for scores was easy.
For compounds I have tried the Radik and the Switch, both by Mission. The Radik is significantly lighter (about 3lbs versus about 4lbs for the Switch), which would make a huge difference for an 8 year old in my opinion. My 12 year old pulls 45lbs draw weight on a Switch with a 26" DL. They build the strength insanely fast if they practice consistently.