Anything you put through an airbrush should be the consistency of milk. If you are using pigments and paints not designed for airbrushing (such as airbrush t-shirt paint, or model paint), then straining the paint first is preferable.

You might want to look into using acrylics instead. I use acrylics in my airbrush almost exclusively. They are easy to thin and pretty forgiving. I use denatured alcohol for cleaning between colors, and for cleaning afterward. If any residue is left in the brush, soaking the parts overnight in DA will also loosen it up.