My notions of chicken keeping has changed *dramatically* from when I began in May.
That very often happens. Portions probably will again.
IF you could start from scratch with something like this; what would you do inside?
How many total chickens? Flock make-up: just hens, hens and a rooster, will you have baby chicks either in a brooder or raised by a broody? What are your goals: eggs, meat, eye candy, bug patrol, a mixture of these or something else?
First let's discuss ventilation. Does that have a ridge vent? In your area you probably won't see enough snow to block a ridge vent if you have one. Those can help a lot with ventilation.
I see you just posted about ventilation so I'll go to the next phase.
I can't go into too much detail unless I know how many chickens and a bit about how you manage them. With a 10 x 12' coop you have enough room to be somewhat flexible.
My first effort would be to determine where the floor level is, including bedding. Then I'd position a pop door high enough that the bedding won't be kicked out but reasonably low. I'd want access to the pop door from inside the coop and outside. I find that a 12" x 12" pop door will be plenty big enough for any chicken. I want to use a smaller pop door instead of the human door as that keeps a lot of weather out of the coop.
Then I position the nests. The rule of thumb is one nest for every 4 hens with a minimum of two nests. So two hens is two nests. Eight hens is two nests. Nine hens is three nests. Most hens will probably use the same nest but an extra nest gives you options if you have issues. I don't plan for everything to always go perfectly. I like flexibility when I have to deal with issues.
Some people put the nests at floor level. Some like the nests high enough so they don't have to bend over that much to gather eggs, that makes it easier if you have a bad back. In my opinion, the chickens don't seem to mind whatever you do. I have two nests about 2 feet off of the floor with two more nest above them at about 4 feet off of the floor.
I don't want my nests to become ovens on hot sunny days. If you have shade this may not apply but in North Carolina the hottest directions will typically be south and west. I don't know how your coop is oriented but I'd want my nests on the north or east side of the coop. With my walk-in coop I like gathering eggs from inside of the coop. I know a lot of people like to gather them from the outside but I've found snakes, dead chickens, and even a possum one time by going inside that I would have probably missed if I was gathering the eggs from outside. However you do it, give yourself access.
I make the roosts noticeably higher than the nests so they are not as likely to sleep in the nests. In a coop your size I'd want the roosts a minimum of 12" higher than anything else you don't want them sleeping on or in.
You say you want a droppings board. There are a lot of different styles of droppings boards. Some have recessed bottoms that hold sand or some other media. Mine is a flat board that I scrape. Consider how you are going to clean it to determine how much room you need to access it below the roosts.
I like the roosts out of the way when I'm inside. I don't like to bump into poopy roosts. With mine that means along the back wall but in your size you can put the roosts along one side. I don't worry about the heat from the sun for roosts. By the time they roost the sun is going down and it has started to cool off.
In winter I like the ventilation over their heads so they are not caught in a crosswind when it is really cold and windy. In summer I don't worry about it. A cool breeze hitting them might feel good.
Some of us feed and/or water in the coop only. Some in the run only. Some of us have food and water in both the coop and run. We all come up with our own reasons and rationalizations on how we want to do this. I almost always have immature chickens in the flock so I feed and water in the coop and have two or three water and feed stations outside.
That's about it for the basics. Depending in how you manage them and your flock make-up you can have specialty items. I have a built-in brooder where I put chicks straight from the incubator or post office. I can use that as a broody buster if it does not have chicks in it. I have a juvenile roost so the young have a place to sleep that is not my nests since they won't sleep on the main roosts with the adults.
Good luck!