When I showed Paints, my routine was shampoo with Orvus, then one round of Quiksilver everywhere, a 2nd round of Quiksilver on the legs & white tail if needed, then Showsheen everywhere except where saddle goes. Once dry, it's sheet, sleazy/hood, and polo wraps to keep 'em gleaming. But those grooming products are VERY drying to the hair, and dry hair will absorb stains even faster, so I highly suggest NOT using them for regular grooming.
Soft, moisturized hair doesn't absorb dirt and nastiness as fast so they'll look and feel cleaner longer if you use a moisturizing shampoo like Lucky Braids All-In-One Shampoo or EZ All Anti-Allergen. Through the years my dark colored horses occasionally got cheated with cheapo human shampoo like VO5, but whites need the good stuff every time to keep cleaner, IMO! I top dress all colors of horses with Healthy Haircare Moisturizer every other day or so to keep the hair moisturized and repelling gunk.
I've found Miracle Groom or Lucky Braids Whitener & Dry Wash Shampoo are decent quick fixes for a stain, or when the weather doesn't allow for a bath.