First, one has to have in mind what kind of animal they want to keep. Certain animals are less demanding of fence. Cattle are relatively undemanding and respectful electric fence; they can be easily kept in with a single strand of electric wire or polywire (polymer fiber rope with thin conductive wire, usually tin plated copper or stainless steel, braided into it). Cattle seem to have better vision of fences than horses, so polywire, which is more visible, should be used with horses.
Goats and sheep are a different story. Both of these animals are more naturally resistant to the shock of an electric fence, and so are less respectful. Both are shorter (and their offspring are very short) requiring electric fence to be much closer to the ground, which increases the ground shorting potential of plants growing in the fence line. And goats especially are agile and clever.
Pigs are very respectful of electric fence, but are strong and destructive as well as clever. They can be very hard on any non-electrified fence, and barb wire shouldn’t be used with pigs.
Poultry can usually fly right over a fence if they want to, but can generally be kept in with modern electric netting. I’ve also found adult chickens can be kept in with sufficiently tight and high woven wire (39-9-6-14 keeps them in) if you clip their wings. That stands for 39” tall, 9 horizontal wires, 6 inch vertical stay spacing, 14 gauge wire, which is about 1/3rd the cost of electric poultry netting per foot and is much longer lasting, but not portable.
Now, if a major consideration is exclusion, let’s say, of coyotes, you will need something that can resist them. I have never had coyote prints inside my fence since I installed it, so I know it works so far. It is a 39-9-6-14 high tensile woven wire fence with a top strand of smooth, electrified low-tensile 14 gauge wire about 7 inches from the top wire of the woven-wire. I also have a strand of barb wire at ground level about an inch below the bottom strand of the woven wire. This resists digging.
Historically, all of these animals have been kept in with locally available materials or plants. Hedges have not only kept in bulls, but reportedly kept out tanks. Stone walls can be effective, too, if built and maintained correctly. Obviously, such living or natural fencing is far less expensive and more environmentally benign than any type of manufactured and erected fence, but it has one major weakness…the relatively long time it takes to develop into an effective barrier. I have used my hybrid fence extensively on my farm, but I partially regret it, and I am experimenting with different methods and strategies which involve living fences.