We have 2 nigerian dwarfs in our suburban backyard, too - 1/4 acre, just like you. I have a shed, it's for keeping my mower and a couple of bales of hay in (and a bunch of other junk that won't fit in the garage, but that's another story). The goats have a separate fenced off pen, about 20x30, and their shelter in the pen is just one of those cattle panel and tarp shelters, with one end blocked off (search for cattle panel . I guess we don't really live in a very harsh climate here in the pacific NW (maybe gets below freezing once or twice a year, rarely snows if ever, and my yard is well sheltered from wind by all my trees). They do just fine in there. We only have wethers, so no milking, but you could just set up a portion of your shed just for your own comfort while milking, and have them actually live on a dirt floor elsewhere. We let ours out to wander the yard and browse around when it's not raining.
Good luck! Keep it simple, and it's all going to work out fine.
Good luck! Keep it simple, and it's all going to work out fine.