It sounds like to me that you are looking for a neutral tasting fat on the saturated fat side of the spectrum (though maybe you are specific to animal fats). Unfortunately, I don't think there is one (at least to my knowledge) that doesn't impart some flavor.
Animal fats I have personally tried are lard/leaf-lard, tallow, buffalo, chicken fat, and duck (duck is really good!). Though not an animal fat, coconut oil falls into this category of saturated fats (actually more saturated than those above with tallow being next in line). If you get virgin coconut oil (not expeller pressed) the flavor imparted onto the food can be pretty minimal. Oh, and there's also MCT oil which is made from coconut oil which is flavorless but large amounts of this I feel make the food taste like it comes from a health food store ;P
I usually like to cook meats in their corresponding fats. Pork in lard, Beef in tallow, etc.
As for other things, I usually use tallow (from grass-fed cows) and lard (from pasture raised pigs)