I've also used only water on ds until recently. Now he is one FILTHY little man come bedtime so I do the same stuff I use for me. Baking soda and apple cider vinegar for hair and body wash. I make a body butter for moisturizing, but any food grade oil will work (olive, coconut, etc). I've heard that the BS can sting the eyes (tho I've never experienced that) so I treat it as though it were shampoo (rinse carefully) and I put the acv into a spray bottle and apply it to ds' wet hair after he's out of the tub.
I do water wash too til the babes get to the age they actually get "dirty". If there's a really yucky blowout or something, we wash with a bit of lather from my handmade castile soap. If using it on ds's hair, I just add a tiny bit of suds with my hands and after rinsing also apply a dilute vinegar rinse with my hands.
Olive oil is good, especially evoo. It can be infused with herbs like chamomile and calendula to make a nice all-purpose rash oil or salve. I like the texture/lightness of coconut oil but find that it can feel somewhat drying, so I use it in combination with other oils.
We rarely use soap on DS. Sometimes if he's gotten really yukky I'll use either Burt's Bees soap, or a tiny bit of my Jason shampoo. Otherwise it's just water for us (me too usually.) He and I both brush our teeth with water and baking soda.
Oh but nowadays he likes to play with the bar of soap in his bath, so I guess he gets some soap on him that way.