Trees, cars, the neighbors' trees and cars ... and yet, goats have a lot to recommend them - they will eat a lot of the weeds and harder grasses you can't get a cow to give a sideways glance at. The fence thing - I never found a fence they couldn't and wouldn't climb or push through, unless it was electric. I loved them (had mostly cashmeres and a few nigerian dwarfs) for the improvements they brought to our property, and hated that I could not keep them in a fence. Never tried to milk them.
I always thought a mini cow sounded ideal, myself, and yes I imagine a milking stand for a cow would have to be a lot sturdier than one for a goat. Never considered sheep - the only ones I've had any exposure to were noisy and smelly, and this is from the perspective of a person who doesn't even notice chicken and goat odor (except a billy, ugh), and does not mind the smell of horse and cow manure, in fact horse manure makes me nostalgic. I don't have the time and resources right now to add any kind of large animal so it's only a future issue for me, but it never hurts to have discussion and learning so I can think through what I might want some day down the road.