For watercolor, I use India Ink - it's my fave. You can use it with any waterbased product like markers or watercolor.
Sharpies are solvent based very much like Stazon so you can use them in some of the same applications.
You can use SU white for Copics, it just takes longer to blend - I use it a lot. Thanks to pinefeather, I also really love the look of Copics on kraft cardstock.