Birds are just about the easiest and cheapest way to set up a livestock industry. They require next to no oversight, don't require a pasture to live, and automatically make food for you every whenever. Eggs have to be cooked to be eaten, but you'll likely be cooking anyway. No problem here. Their breeding is also very easy to control.
What birds lack in the livestock industry, however, is versatility. They produce food and nothing but. Contrast to goats, cows, donkeys, horses, sheep, etc.: These all produce milk, which can be made into the much higher-quality cheese, and yield higher amounts of resources when butchered. Getting a cheese industry running, however, takes a lot of workshop micromanagement, require a pasture, and will waste a lot of time on the workshop that milks these animals and processes it. If you plan on making cheese, I highly recommend you make an extra farmer workshop or two. Consider streamlining the process with an assembly line approach. Sheep produce wool, so they are a great way to kickstart a cloth industry as well, but double the micromanagement involved as well. If you plan to run a fortress without a farm, then I'd recommend you bring a few sheep. Alpacas and llamas produce wool and milk as well.
Also, cows are just plain expensive. Don't buy them.
Your choice of embark location may also influence your choice of animal to farm. Don't bring grazing animals to dangerous biomes or those with little or no vegetation. It is worth noting that pigs don't graze, yet still produce milk.