Welcome!
My flock is comprised entirely of different breeds. It's colorful! They can all be housed together. I even have two ducks with my flock of 9 grown chickens. I have six more chicks about 12 wks old in a segregation coop/run, because it's best to introduce those once they're closer to the same size as the original flock.
You would be best to combine the chicks NOW and let them get their pecking order established. Yes, it's tough for some of us to observe that process, but trust me, it will be worse if they don't do it until they are older.
ANY manner of coop will do for chickens; it's really us people who have opinions and desires about how they look!
All they need is security against predators, a place to sleep (on roost bars), a safe place to lay eggs, good food and water, and some yard space for daytime chicken activities. Polo, soccer, jump rope, baseball and the like. (Just kidding.) But they do need about 10 sq feet per chicken in the run.
If you do have the room, and the materials, make your coop and run large enough for expansion. Once you get to know your chicks as they grow, you will probably become enamored of them, start studying up on breeds, and want to add more to your flock.