Regular shampoo is just fine for youngsters, you just want to use something that's very gentle. I'd highly recommend the Earthbath line of dog shampoo, it's soap-free (so not overly drying) and has no harmful chemicals. There are several formulas, we use the Oatmeal and Aloe kind since Caney has sensitive skin/allergies, but they make one especially for puppies too that's tear-free.

I get Earthbath from PetCo, but I've seen it at just about all of the smaller pet supply chains and independent stores near me too. PetSmart on the other hand has stopped carrying Earthbath products (at least all the stores in my area have). :(