My own personal thoughts are that children should spend several years enjoying music, being exposed to a variety and when and if the spark strikes, to take on more formal music lessons. From my experience, don't rush it and start too early unless there is a strong interest.
When the child is ready {or you're ready to prod him forward!}, here are some thoughts on finding a match:
Traits of a Great Music Teacher:
:: your child will like him!
:: he will make clear what methods used and why
:: she will encourage regular practice
:: she will encourage your child to play music they like as well as other styles
:: he will give an opportunity for the children to display their efforts at a recital or some other format
:: for beginners, he will encourage the parent to sit in the lesson or may record the lesson for the parent to review at home.
:: she will give opportunity for the students to hear her play
I loved my piano and violin teachers! The same Japenese woman instructed me in violin from age 9 until age 17--she had a significant impact on my childhood years, wouldn't you think? It was at her home that I first ate octopus.
I did not know it was octopus.
She told me it tasted like chicken. Why do people always say that!?
It was also the last time I tried octopus.
But, anyway...back to musical thoughts! I appreciated her so much :: and our piano teacher as well. So when seeking out an instructor for your children--consider personality as well. They may be the best or the cheapest or whatever...but if your child doesn't click with him, it could ruin their appetite for music lessons for good.
Not worth it!