I assume I want raw meat, fat, and tallow, but what else? Bones? Teeth? Hair? Corpses? Also, where can I find all these things in the custom stock pile settings?
While it is possible to specify individually every item allowed into your stockpile, this would be a massive pain because many of the animal body parts (as mentioned in the food stockpile entry) are different per animal. So it would not be a matter of including "fat" as an allowed item in a stockpile; it would require setting "horse fat", "dog fat", "dragon fat", etc. inside the stockpile settings.
Do not despair. There is an easier way to handle this problem. Simply set a stockpile to accept any kind of food and/or refuse, but then link it to your production butcher shop(s) (use the q-t command from the stockpile and select your butcher shop). Finally set the stockpile to only take (accept) from links (the a command from the q menu for the stockpile), and then it will only be filled with items from your butcher workshop. This stockpile's only job is to accept everything from the butcher's workshop.
Warning: Make sure you either link both a refuse and a food stockpile to your butcher shop, or else make a single custom stockpile that does both, because anything that will not fit into the linked stockpile(s) will be stuck in the butcher's workshop.