No expert here, but this is what i did. When my boy was 2 and a half, i bought a Cabelas fiberglass stick with a few fiberglass arrows. It pulls about 5#, and costs about 20$.
When he turned 5, i bought him a K@K Great-tree 48" recurve that pulls 20#. He is 7 now, and shoots well with it. In fact last summer he shot a couple chipmunks. My daughter is 4, and she shoots the Cabelas fiberglass once in a while. It is a joy beyond explanation watching your children learning a sport that you love.