Eggs get produced so abundantly and birds are so cheap that there's no reason not to use peafowl. I actually prefer geese. They mature in one year, produce less eggs but slightly more meat, and geese are just much cooler (have you heard the sort of noises peacocks make? I hate the bastards).
Keep in mind that an egg is 1 unit of food, size is irrelevant. This means that ducks and guineafowl, which are too small to butcher, are actually the best traditional poultry for egg production, since they lay large clutches. Ducks lay the largest clutches, but take 2 years to mature. Guineafowl begin laying after 1 year, and produce almost as many eggs. For truly excessive egg production, you want reptiles, since they lay huge clutches. Cave crocodiles (obtainable via traps in the caverns and an animal trainer) are high value (4x multiplier), produce a lot of meat, and lay 20 to 60 eggs at a time! The only disadvantage is that they take 3 years to mature, but with clutches so large, in 3 years you will have fps crippling numbers of enormous, delicious crocodiles. You will have so much high value food that by the time the goblins hear the rumors of your excessive wealth, your dwarves will be spherical balls of pampered lard. Thankfully, you will have a few hundred cave crocodiles to devour any invaders.
In recent versions, since fruit is harvestable, there's really no excuse not to be absolutely swimming in booze, if you have fruit trees on your site.
Make some max size zones, set them for gathering (you can also pasture animals there), and throughout the summer you will get several hundred units of fruit, more if you really try. By the time the first caravan arrives, you can have more booze than you know what to do with. Always keep an excessive booze stockpile, so that if disaster happens and production halts, it will be years until your dwarves go sober. Once a fortress gets properly up and running, I get worried if booze stocks go below 1000.
Herbalism also provides quite a bit of food, to supplement your eggs. Herbalism is really the best skill for early fortress food ad booze production. Bring a proficient herbalist on embark, let him do his thing, and feel free to not worry about food for years, giving you plenty of time to figure out traditional agriculture before the goblins start making problems for your herbalists.
As far as livestock goes, for simplicity stick to nongrazers. Pigs are relatively cheap, provide abundant meat, milk, leather, and bones, and keeping them is as simple as shutting them in a large room and not slaughtering them so much that they die out. Dogs are another good choice. They provide almost as much food as pigs, and though they aren't milkable, you can train them for war. War dogs have never been very deadly, recent versions being particularly bad, but they are still useful for pasturing at entrances to detect thieves, necromancers, and snatchers, and when assigned to military dwarves, provide more non dwarf targets for enemies to waste time on while your soldiers do the actual killing.
Grazers are nice, but require pasture space, which means you have to secure a portion of the surface or caverns against attack, or go through the time and effort to grow your own pastures in a secure location. Sheep and alpacas are probably the most practical (shearable, milkable, decent butchering returns, low pasture requirements), but I must admit I have a terrible fondness for reindeer and water buffalo.
Basically, farming is completely unnecessary. I got bored of it a few years ago, and have succesfully run many many fortresses without planting a single crop. Farming is very productive, not much work, and siege proof. It's a good thing to learn how to do correctly. But don't feel like you have to make it work immediately. There's no reason to go hungry or sober while you figure out agriculture.
(It just occurred to me that your problem might be storage. Make a lot of barrels. If you have trouble making enough, recruit a stonecrafter and set rock pots on repeat. You will need a lot, and barrel shortage is the best way to have an excessive food income but hungry, sober dwarves. Don't let it happen to you.)