The nests are referred to as Lairs, and they are automatically spread on the map unless you select the "No Lairs" option.
Starting with Barbarian World means some areas of the map contain cultural borders at the beginning, so it reduces the space available for Lairs and Animals to spawn in.
Also, Barbarians and Animals both count against the total limit for how many barbarians may be in the game at a time (based on number of tiles not revealed by any player), thus having Barbarian World selected means there are Barb cities, and thus Barb defenders, and there will be fewer available slots for animals to occupy in that limit.
Raging Barbarian's ought to be a safe option to have and not affect your number of animals available directly, but I am not entirely certain what this option affects quite yet. I except that it makes the Barbarian's more likely to attack, which means animals would attack more often, and thus die to the AI scouts frequently. It could also make it so that each barbarian city is able to produce units quicker, which would mean once again you are filling the available slots with Barbarians instead of Animals.
So for the most possible animals, avoid Barbarian World for certain. Raging Barbarians may be safe, but is quite unlikely to result in MORE animals, and fairly likely to result in fewer; thus you probably ought to avoid it as well to improve your chances.