I'm referring to if animals should be in a group, should they be kept in pairs, or if they can be kept in single-sex groups.
This is more complicated than just looking up online how the animals live in the wild. For example, many ruminants live in the wild in large herds with multiple males, but a key factor is that the herd is spread out over a large area, giving the males the ability to flee from each other and thus to avoid conflicts that could otherwise be dangerous. This isn't always possible in a zoo, depending on the intra-species flight distance and the size of the enclosure, so a species that exists in the wild with multiple males in a herd might have only one male in a zoo group to avoid fatal conflicts. (With some species, you can manage to have two males if there is a dense copse or a hill in the enclosure of sufficient size and strategically placed, which enables the less dominant male to get out of the sight of the dominant male.) All of this is also true for many species of primates. This requires more in-depth research to find the experience with a particular species in captivity, which isn't always easy.
I can tell you from my own experience that for species that exist in the wild in groups with more than one of both sexes, it can in fact be very difficult or impossible to find out what's considered the appropriate or ideal group size and sex ratio for a group in captivity. For my fantasy zoo, I basically had to make educated guesses for species that include reindeer/caribou, wolves, rabbits and hares, many rodents, shrews, sea otters, dolphins and porpoises, and many species of bats. (Indeed, the mating system and wild sex ratios are utterly unknown to science for the vast majority of bat species and at best poorly known for many rodents and shrews.) Bears in the wild are solitary except for brief breeding encounters and situations like salmon runs or shore assemblages of Polar Bears when there is no pack ice but there has been good success housing bears in captivity in single sex groups of 2 or 3. The latter makes for a more interesting exhibit, but is it "natural"? At least some, if not most, fox species are solitary for part of the year but come together as pairs for the breeding season and to raise the kits, and sometimes for even more than that. So what do you do in a zoo? It's simplest to exhibit them as pairs year round, which will generally work.
It is considerably easier to get the wild information for birds on-line than for mammals, and there is tremendous detail about how they live in the wild in birdsoftheworld.org. Most birds of course live in the wild as pairs and the information on typical/average nest-to-nest difference will tell you whether in captivity you can house more than one pair in the space you have available. But there are lots of questions to which you can't find the answers, like what's a good size and sex ratio for a captive group of tinamous or rheas?
There is also a dearth of information on line for most species of reptiles and amphibians. I basically just decided on a rule of thumb to display (a) most reptiles in pairs, and (b) most amphibians in groups of 2.2 since for the latter the presence of more than one male is often tied to reproductive success. Exceptions are made of course for species that are known to be aggressively territorial or for unique situations like the Helmeted Water Toad where the females are much larger than the males and will eat them.