The larger the cage is, the more room they will have for exercise. There should be at least two perches but not so many that there is no room to fly. Don t use a perch with sand paper on it. This is too hard on their feet. Consider how easy it is to clean, how well it contain the mess of seeds flying, and how easy it is to catch a bird.
Zebras like to spend the night in a nest.
This is not a requirement. One thing to keep in mind, if there is a nest, they will breed and lay eggs. If you do not want babies, do not buy a nest. You can buy a nest from the pet store. The most common for Zebras is the enclosed wicker nest with a front opening hole.