Trooper is almost 5 months old (wow did I just say that?). Up until this last bath I used what the breeder recommended to me, because she knows her puppies and her coats, which was Herbal Essence Hello Hydration (yes, the human kind). Lately he's been a "go outside and play in the dirt" kind of dog, so I bought a whitening shampoo and a good conditioner. What I wanted to buy wasn't available locally, so I got something else, which I LOVE (except for the scent of the conditioner, lol)!
So, a good place to start would be to ask your breeder. He/she should know what has always worked well for their puppies' coats. Many of them have probably literally tried every brand out there and have a go-to favorite that they find works for their puppies. Next, if you want to switch, it's just a matter of trial and error until you find a combo you like. I'm pretty sure it doesn't really matter if you use adult or puppy shampoo, as long as there aren't harsh chemicals (some whitening ones have bleach, I've read, YUCK). That said there are "puppy" versions out there. Biogroom makes a "Fluffy Puppy" one, for instance, though I never tried it ever, just giving an example.
Keep in mind that you may find products that look appealing online, or you've heard some of us use, but it's also going to depend on if you're ok ordering it or if you need it right away. I found that local supply is pretty hit and miss around here. I was looking for something particular on Friday that I never did find around here.
I needed it that day or I would have just ordered it.
Sorry for the long winded post. Hope this helps.