Honestly, whatever makes the most sense with the materials in the local area. And then I don't mean what you can get from the local hardware store, but literally, what the earth in the area provides. If you have lots of clay, then brick would be best. If you have lots of big stones, then stone construction it'll be. If you're deep in the woods, then a wooden building would serve you just right. Maybe a combination of materials and techniques if you have options in the area.
Bonus points if you can build in a way that passively optimises for managing things like moisture and temperature.
I would guess that a culture built by &/or for winged people would have more strapless stuff. Or from the chest over the shoulders and tied up behind the neck. Or otherwise designed to not interfere and/or interact with the wings.