It is a very good question. I think there are two basic ways to approach when you are depicting animals. One is using the animal's anatomy, maybe distorting it a bit or emphasizing certain body parts while simplifying certain features. It really depends on what the character's role is. What is the story about? The other approach is basically using human, or mostly human body features with an animal's head. Both are acceptable and popular. If you can take a look at @Jake-Parker 's work, you can see how he is using both on a mastery level.
For picture books, even though the animals are often highly "designed" and act like humans, illustrators often keep the animal's body features too. But it depends, and actually you can use it as a tool in your storytelling. If the story has humans too, e.g.: Goldilocks, I would keep the bears very bear like to emphasize the difference between them and the girl.
On the other hand, in comic books or books for older children animals often have human bodies, perhaps some features ( claws, tail) are kept, but basically they are standing on two legs and walking and acting like humans. To me, they rather represent a human heroes, who are acting out their "spirit animals".
Uh, rereading your lines I am not sure I have answered your question. Perhaps it referred to the technical side. I try to rephrase it:
How can a half animal half human character, or an anthropomophic animal look great and consistent? (As if all the body parts belonged together, not like somebody randomly stitched a head, a body and some limbs together? 
SVS learn has a fantastic "Drawing Animals" course, one of the exercises asks you to draw a real animal study, then different stylized versions. It is a not only a fun exercise but will change how you se things and a huge help to understand character design. Copying other illustrators' animal characters and trying to grasp why certain parts look as they look could be also useful .
From SVS: The Posing Characters, Heroes and Sidekicks and How to Draw Everything are fantastic sources too.
I hope it helps.
we might go for a Sketch Crawl.