What's your purpose? For Collection of Community Center the answer is Y, and maybe Coop is better. Because compared with the Truffles, the duck feather and rabbit root are really hard to get. For money.......Does really Animal Products can make money?
I generally go coop first cause rabbit feet and duck feather are a pain to get unless you are lucky with the wagon person. Also cause the chickens are adorable. Getting truffles can also be a pain but I find that since pigs are the last thing you unlock its an expensive process so its just easier to do that one later on when you are consistently making more money to afford the upgrades and such.
Coop is the easiest way to get into animal goods, it's a lot nicer to your wallet. You can eventually incubate eggs so you dont have to buy more animals, and they don't require you buy a bucket or shears. Just make sure to have a field of grass for them to graze in, it's worth the time and space it takes. Make sure to pet them every day too! Its way easier to pet them if you close the pet door thing they come out of every night and pet them BEFORE you let them out to graze. Good luck!
Coop, for a couple reasons. The animals for a coop are cheaper, so are easier to obtain earlier on; also, two animals in the coop (the rabbit and the duck) have drops based on happiness so getting them as early as possible is really helpful. You won't be able to get the duck or rabbit until you upgrade the coop some, so that won't be immediately helpful, but it should be noted as you build your animal area.
Coop is better at the begining imo. Milking and shearing will cost you money and energy, while at the begining of the game, you will have both troubles. You will spend most of your energy on farming and animal husbandry, and not enough on anything else like forestry, mining, and fishing. Especially when you woke up with half full energy after late sleeping in the previous night.
Actually, I'd buck the trend and say Barn first. Cheese is a VERY good hp/energy food which can help you get much further in the mines. Mayo is appropriately inedible.
