Well the only inks I know of that work with Copics are Memento and Adirondack. Here's what I would do: Have brown/black/grey inkpads in either Memento or Adirondack for stamps you are going to color with Copics (after all, how many times are you going to use lettuce green to stamp an outline?).
The rest would be colored inks from Impress or Amuse Studios. Their quick dry pigment inks are absolutely, hands down, fantastic for all kinds of stamps and paper! I use a combination of clear and rubber stamps, and always had trouble with inks for clear stamps. But Fresh Inks and Amuse inks give me crisp, clear, vibrant impression all the time. I love 'em and when I get ALL the colors eventually, I'm tossing all my other dye inks.