I'll try to offer some help.
First off, determine if he is left eye or right eye dominate. That will save you some trouble down the road. To do this, have him stand about 10 feet away from you with his arms straight out, fingers pointing up and palms facing you. Have him overlap his fingers to create a small hole above the thumbs. While he looks at you through the hole have him slowly bring his hands back to his face. You will notice when he gets near his eyes the hands will go either towards the right eye or left eye. Thats the dominate eye.

A real simple method to check his draw lenght is to once again have him hold his arms straight out but this time palms together. Take a yard stick and measure the distance between his throat and tips of his fingers.

Draw weight is the toughest to determine because I don't know how strong he is.

There a lot of good youth bows on the market, almost all the manufactures have them. The biggest thing is getting one that fits him and has the range of adjustments as he continues to grows. I like the Browning Micro Midas. I've bought 2, A LH for my son and pick up a RH at a yard sale for neighbor kids who come over to shoot. The current MM3 has a draw weight range of 20 to 30 lbs. which should work for you and it has a draw length of 18" to 28" which will keep him slinging arrows as he grows. The instructions on making adjustments are real easy to read and understand.

I'm not sure what your price range might be but Cabela's has package deals you might like and Ebay has a lot of new youth bows.

Hope that helps.