I would make sure to have room for human access to the chicken run, incase of stray eggs in the run. I agree to get broody breeds and a rooster to do the work for you. We have a rotational run for our chickens- a main on that comes off the coop and a couple that branch out from it. It also butts up around our garden area so that weeds that are pulled can be thrown in for them during when we are growing. We also have a 'chicken door' in our fence to let the chickens in and out of the garden when we want them to eat weeds. We haven't been doing that lately because we have a hawk that watches them in the garden, like, well a hawk. Their run is in the middle of our property and was a wooded area at one time, and there are still a good number of deciduous trees, so this time of year they have plenty of shade, and during the winter they get light. And the trees help deter the hawks then.
We have our 'juvenile' chicken run adjacent. When get a broody, we move her nest and all. It's a 'annex' on our main coop with an open window into the coop separated with hardware cloth. Baby chicks can still get thru chicken wire. They can see each other but none of the other hens can add to the nest or mess with it. The roof lifts up and there is a pop-door that we open during the day so mama can move around if she wants to. We have it totally covered with chicken wire, as the younger birds tend to be 'flightier'. And it's 'skirted' with hardware cloth. Our regular chicken run fencing is 6 ft. and they do still find their way over it sometimes, though. But I agree about being able to keep your chickens with your goats, it will help with the parasites. Hindsight is 20/20. We've had chickens for years and our barn we didn't build to last year.
We have meat rabbits in 1 section of our barn. Also the same size as yours, 20 x 30. We did a cement floor, thinking it would be easier to clean. One of our projects currently is "Where are we going to move the rabbits because animal poop and cement was a terrible idea." We hose, sweep, and shopvac the rabbits weekly. It's disgusting. We also have rubbermaid totes set up under their hutches, with shower curtains hanging off the bottom of their cages to 'funnel' the poop and pee into the tote. It's still a gross mess.
I like your goat layout. It's similar to my friends, but all she has is goats in her barn and her barn is much bigger and it works great. Our barn is divided into 3 sections- the 'bunny barn', the middle, we call the 'barn' where we have our feed, hay and other animal supplies, extra feeders waterers etc. The 3rd section, the 'goat barn' the fence runs the length of the barn in the middle of their section. We have 3 goats. They have plenty of room to walk around, sleep stay dry etc. On the people side of the goat fence in the barn, we have our kidding stall and milking stand right there. This worked great for us because all the goats were still together during kidding, and were able to get used to the kids and we had no 'introduction' problems, no goats alone. Having the milk stand in the goat area worked great because if we'd had the milking area in the main part, she'd go running for the hay. We also use the milk stand for our bucks to administer shots or supplements when needed and to trim hooves. One thing to mention though, is our younger bucks horns will no longer fit thru the top of the milk stand, so that's something to consider.
We don't have a sink in the barn. Our milking routine is like this. Get pot with a cup of warm water and couple of clean 'goat rags' in the house. We go out to the barn, get the goat on the stand, hobble her legs, and we keep a pump-dispenser of very diluted hand soap under the stand. Couple of pumps on our hands before we start milking, wipe them on one rag. Dip another rag in the water from the house, wipe off teats. Milk into the pail. Cover, and go sit it on the freezer in the main part that has feed in it. Go put the goat back in with the others. Take the milk into the house, where sometimes someone else will strain it and put it in the fridge and sometimes not, then we go do the other critter chores.
So that works for us. What doesn't work again is the cement floor. We have rotational runs for the chickens. We have the same with the goats. We also have a solar powered electric fence on the goat and have never had a problem. What would I chan ge about our current set up? My barn would be BIGGER. It's not big enough. We to did the door big enough to drive a tractor in, for when we get a tractor. After we got the feed freezers in there, and a chicken brooder that we only use now for sick or injured birds, and hay.... no room for a tractor. I'd have a barn cat or 2 for the mice and snakes that now love our barn. (We have dogs. That eat cats. My advice is get a cat before dogs).
So that's my 2 cents.