The great thing about the basic cyanotype is how safe it is for kids to have a go. I use the method described in Christopher James' book: The Book of Alternative Photographic Processes (ISBN 0-7668-2077-7), or use the technique on the Alternative Photography Web site. I don't find it necessary to use distilled or de-ionised water even though we live in a hard water area with chlorine added.
I normally use a few drops of hydrogen peroxide in the final rinse to get a nice deep blue. I've tried other toners but they all seem a bit muddy in their effect.
I am poised to try the New Cyanotype, but the chemicals are not as safe as the traditional method, so this isn't one for the children.