As far as shampoos are concerned...
Johnson's Baby Shampoo works great unless dealing with a very greasy coat...then we use Dawn Dishwashing liquid. If it's safe for oil-soaked Ducks and Shore birds it's good enough for dogs.
BTW, no matter what you use for shampooing, make sure you rinse it ALL off...then rinse again to make sure. ANY residue can react with skin and cause itching, irritation, hot spots. That's why we like Dawn so much...excellent rinsing qualities.