I have used soap/water, and I've used a QD as well. Either way, I don't wash after that step. I just wipe it off with a MF towel. There may some residue left over, but when you apply a polish or a cleaner, you will remove any residue left behind by the clay/QD.
When I use soap and water, I put about a dime-sized spot of car soap in a spray bottle, and fill the rest with distilled water. That way you won't have to worry about any hard water spots on the vehicle.