Looking at building order, you'll want to start with a silo right away - costs just 100g and some basic materials but lets you store hay which is crucial before getting any animals. Once that's done grab a basic coop since the material requirements are pretty manageable, and chickens give you early income through mayo production. Keep an eye on robin's shop schedule, she needs 2 days to finish each building and won't work on festival days.

The barn should be your next priority especially since dairy products are more profitable than eggs - cows take longer to mature but cheese sells for significantly more than mayo. As you expand, you'll want to get those deluxe upgrades going which add auto-feeders and unlock new animals, just time the upgrades around your gold income since they get expensive. The building animations actually show progress over the construction period which is a neat detail to watch.

For mid-game optimization grab some sheds once you have artisan equipment since they give you 67 spaces to work with, really efficient for kegs and preserve jars. Wells are useful early but become obsolete once you have quality sprinklers set up. Fish ponds and the mill are totally optional - ponds help with bundle items but aren't great money makers, and the mill is mainly for processing wheat which isn't a top crop anyway. The stable costs 100 hardwood which is rough to get early, but that horse speed boost saves about an hour and a half of walking time each day once you can afford it.