Once you begin living off the land and start using and rendering fat from animals you kill, you learn quickly that all fats are not created equal. One property of rendered fats that is of importance is the smoke point. Different fats/oils have different smoke points. Low or high smoke points will determine what is a good end use of your fat/oils. If your oil makes a lot of smoke when it is burned then that isn't going to be a good choice for an indoor light.
You can generally tell whether a fat you have never dealt with is going to be a "good" or a "bad" fat/oil simply by holding it. The softer the fat the better the oil it will produce.
So which fats should you use! Well chances are you will be using all you can get and the sources are vast so instead of trying to list or rank the different fats and the oils they can be turned into, instead I will just try to lay down some guidelines to point you in the right direction.
The best oils from animals are what you would want for a lamp. The worst or most smokey oils you would use outside in torches typically. All fat is not created equal and marine mammals produce some of the absolute best. Whales would probably be at the top of the list. But chances are you aren't going to be hunting whales but if you live by the sea and a dead one washes up, don't let the opportunity pass you by!
So in general the cold water mammals make good oil. So think seals and such. But also turtles are another good source of fat/oil. The fat from ducks and geese are less dense and easier to melt and make excellent oils for cooking!
Keep in mind that a single animal can have both good and not so good fat. Fat from different parts of an animal can be entirely different than fats from a different part of the same animal. So you can't just lump all fat from a single animal as the same. Time and experience will teach you all you need to know.
Any animal fat can be rendered into something useful. And that will be your main source of oils initially. But pressing a plant (usually seed) into oils makes great oils. Plant fats are usuaally going to be less dense and a better source for oil than most animal fats.
Deer, hogs, raccoons, possums, birds all have useful fat and that is likely to be your first source of oils. So any animal you kill for food can also supply you with some amount of light for those dark nights that we as a civilized people have managed to almost completely avoid.
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