The must-haves are the basics; protection from the environment, protection from predators, good ventilation, draft protection, pop door, people door for your size coop, roosts and nests. I feed and water in the coop as well as in the run, not everybody does. Knowing more about how you are going to manage your chickens might spark some ideas, things like will broody hens raise chicks with the flock or will you be brooding chicks yourself.
I built my brooder into the coop. It’s 3’ x 6’. The chicks go into it straight from the incubator. I wish I’d made it 8’ long instead so it would stretch all the way across that wall since I use the top as a droppings board. That’s a big recommendation, put in a droppings board to help you manage the poop load in there. I scrape mine anywhere from once a week to once every three weeks, depending on how many chickens I have in here and how wet the weather is. If it is wet and the air humid or I have more chickens I have to do it more often. With dry weather and fewer chickens, not so often. You’ll find your own schedule. It’s not part of the coop but I recommend a compost pile to give you a place to get rid of that poop.
That brooder also serves as a broody buster or a place to isolate an injured chicken. When it is empty I often put mice snap traps in there to help control the mice population.
I see you have some younger chicks so you will be integrating them with the flock. One of the places I see the adults most brutal to younger chicks when integrating, whether I raised them in a brooder or if a broody raised them with the flock and then weaned them, is on the roosts. Often that brutality is bad enough that the chicks look for a safer place to sleep. That can be your nests. That is such a regular occurrence for me that I put in an extra roost, higher than the nests but lower than the main roosts, and horizontally separated from the main roosts to give them a safe place to go other than the nests. That has saved me a whole lot of problems. That extra “juvenile roost” is over my nests and the top of the nests become dropping boards. Don’t get hung up on how many linear inches of roost space you need, you will get recommendations from 8” to well over a foot per bird, but think more of how the weak can get away from the bullies since it sounds like you will be integrating.
I don’t separate my broody hens from the flock, but if you do a place set up for that in the coop is a good idea. My brooder has a wire bottom so it can work as a broody buster, but if you are wanting a hen to hatch you don’t want to cool off her undersides. So two separate areas where you can put chickens, one with a wire bottom and one without. These don’t both have to be in the coop but the coop is predator proof. You don’t have to worry about that if they are in a safe place. One of these can be set up so you can house chicks before integration too, after they are out of the brooder. Two areas gives you a lot more flexibility. You might have chicks in a brooder, a broody hatching eggs, an injured chicken that needs isolation, and a broody you want to bust at the same time. These are not very likely to happen at the same time but two separate places gives you a lot more flexibility than just one. My “second place” is a separate coop at the other end of the run, not in the main coop itself, but with a connection to the run plus an internal fence I can isolate a part of the run with that second coop. I also have a large area enclosed in electric netting with a third isolation place out there. It is not used much but is occasionally has been quite handy.
I made a couple of my nests so I could lock a chicken in there if I want to. That has come in handy a few times. It’s a great place to temporarily stash a chicken for whatever reason or put the chicks while you are working in the brooder. When I’m trying to figure out which pullet or hen is laying which egg, I might lock them in there with no other eggs so I can see what she is laying when I catch her on the nest. When I have a hen laying on the coop floor, when I catch her on her nest in the floor I lock her in the real nest until she lays her egg. I normally only have to do this once (on occasion twice) to retrain her to lay in a nest instead of on the floor.
Another feature I find real useful is that I did not make my main coop as small as I could so I could shoehorn chickens in there. I made it larger than I needed. That made it a lot easier on me to manage and work in there. That’s not so much for the chickens’ benefit though they do get benefits, but to make my life less stressful. All the other things above make it a lot more flexible for me when I have problems to manage, but they would be impossible without extra room. Extra room in the run is really handy too.
I recommend a separate area for storage. That’s not just for feed but for all the other stuff you get for them. That’s extra feeders and waterers for my brooder or for an isolated chicken, heat for the brooder when needed, stuff to treat the chickens when they need it, my mouse snap traps and my other live traps, extra golf balls for fake eggs, just all the stuff you collect.
I also ran electricity and water to the coop. I used a frost free spigot which is real handy, not just for watering the chickens but to wash things as well as irrigating my fruit trees in that area. With the electricity I have lights at night, can heat the chicks in the brooder, and have an outlet for my power tools.
Others will manage their chickens differently, have different set-ups, and have different flock make-ups. A lot of what I have would be wasted on someone keeping four or six hens in a small backyard coop and run and never integrating. We are all unique. My main suggestions are to provide adequate space instead of designing for the absolute minimum, build in as much flexibility into it as you can, and be flexible yourself. Things seldom work out exactly as planned but it is a fun journey.