Don't dye the goatskin after you draw on the leather. That's a disaster waiting to happen. Paste will invariably get onto the surface of the leather - even the most minute amount - and your dye won't 'take' in that area.
I prefer 'aniline' dyes - either Hewit's or Leather Conservation Centre's. The reason why? The both sell fixatives to go along with them. These fixatives are important if you're trying to 'hit' a shade and want to keep that shade. Otherwise some dye stuff will come out in the pasting up/working of the leather. Count on it!
In fact, I've gotten to where I don't buy much tannery dyed skins at all. With several techniques, either hand application or spray gun application, you can vary the surface penetration - almost infinitely. With the fixative, you're then able to lock in the color/shade.
Below are some examples of hand-dyed calf and goat.