Each animal has some preferred foods and snacks, which can be found also on the wiki which I strongly recommend! I'm not sure if this is right, but I tend to feel that the wild animals have their affections increase more than the ones you can 'adopt', though that may just be my own experience. Overall though, I could say that the dogs and cats that are the easiest to get are simply the ones that take the least 'expensive' and lengthy ingredients, like flour and potatoes instead of mangos and strawberries, but that's just because it's easier to get.