My son drinks soy milk. His pediatrician, allergist and nutritionist (from the allergist's office) all recommended that over any other alternative milk products. It is most similar to cow's milk in terms of nutrients, vitamins and fat (which is important when they are little).
yes, I have heard all the controversy and fears about too much soy, but I decided to go with the doctors' recommendations. We buy the non-refrigerated kind at Costco (Kirkland brand) since it lasts for a long time and is cheaper than buying Silk, plus it's organic. He's 5 now and he is all boy, so the estrogen isn't having any negative or noticeable effects on him, at least not yet.
I hadn't heard about the arsenic in rice milk. Interesting. I would have suggested that as a backup to soy. I don't think coconut milk or hemp milk have much nutritional value at all. There is also controversy and debate over whether or not coconut is a tree nut, so I'd watch for a reaction if you decide to try that one.
A few other tips that may help you along the way (we avoid all milk, egg and nuts for my son):
1. His favorite pizza is Amy's brand dairy-free cheeze made with a rice crust
2. His favorite cereal/granola bars (the kind with fruit in the middle, similar to a nutri-grain bar) are either Glutino brand or Barbara's brand
3. Enjoy Life makes pretty good double chocolate cookies
4. "What's to Eat: The Dairy Free, Egg Free, Nut Free Cookbook" has really good recipes for cakes, cookies, and other baked goods (plus regular food too, though we usually just use it for baking)
5. Duncan Hines homestyle original chocolate frosting is dairy-free, as are many of their cake mixes
6. A good egg substitute when baking is to mix together 1.5 TBSP of oil + 1.5 TBSP of water + 1 tsp of baking powder and add the mixture in place of an egg. We've found that it works best when you only need to replace one or two eggs; any more than that and it doesn't come out that well.
Good luck! I hope he outgrows them.
ETA: just read many of the other responses. Be very careful with goat's milk when you first try it, as many people who react to dairy also react to goat's milk. And definitely don't do lactaid. Your child is not lactose intolerant but rather truly allergic to the proteins in milk and drinking lactaid will NOT solve the problem.