At what age do you start brushing the teeth of your children? Do we need to clean their gums before they even begin to have teeth?

I use a wet cloth with boiled lukewarm water to clean my baby's gums for 1st 6mths. Then after that I use normal water. Until 16mth then I start to use a soft brush with toothpaste free of fluoride. I using 1st teeth toothpaste.