I typically just use a good quality "people shampoo" for my dog. When my dog was younger, I would wash her outside with the good 'ol garden hose. This week, I took pity on her and gave her a nice warm bath in the tub. She enjoyed that much more than the hose...
Whatever product you use, be sure to
thoroughly rinse out the shampoo/soap to avoid itchy dry skin. I use an old "dog towel" (towel that is no longer "good enough" for company) to get out as much water as possible. My next step is to use a "slicker" brush to help prevent clumps. Then.. a nice doggie treat for all of her suffering. After the treat, she finishes air-drying outside.
For what it is worth, I had a bad experience with a cat as a small child (I was around 3?). Three delightful parallel scratches down my arm from elbow to wrist. No permanent physical scarring and minimal mental scars, but I definitely prefer dogs - even the pitiful "why don't you love me anymore" look