As you will invariably notice, there’s a difference between what you can apply to an adult dog, and what product you should apply to a puppy. You will find both puppy shampoos and dog shampoos. Before picking one, you had better consult a vet and their opinion on your pet’s immune system. Some shampoos could be extremely dangerous (even lethal) for puppies.
When choosing a shampoo pay special attention to ingredients. While it is ok to buy a shampoo consisting of pyrethin (the most common insecticide ingredient) for a perfectly healthy adult dog that lives outside the house, it will definitely not be ok to buy it for a puppy or a fragile lap dog. The latter group of pets need herbal insecticides, look for shampoos which include oatmeal or tea tree oil.
It may also be a good idea to use a coat conditioner to make sure your pet’s skin won’t stay dry. Be careful about any scent shampoos; scents may further irritate the skin of your flea-infested animal.