Fur, feather and eye.

An animal stands or falls on structure: get the skull wrong and no amount of fur will rescue it. Texture comes after, built in microrealism from short strokes running the way the hair grows or the feather overlaps, so at arm's length it reads as coat even though up close it's loose lines. The eye is the only place that goes to full black, with the highlight saved from the first pass — it's what makes the animal alive rather than taxidermied. If it's your dog or your cat, I need a photo taken at their eye level; the ones shot from above, which is most of them, flatten the muzzle.