Welcome to chickens. They are wonderful pets that can lay your breakfast. I built an 8x10 coop and it's already toooo small....so much for just "5 - 6 birds for fresh eggs"
I have experience with chicks 2 different ages and intigration of those chicks to an exsisting flock. First, take a deep breath. Second, remember they have bird brains and really don't think about things in the depth we do. I tend to put my "new" birds in much earlier than most people do....about 4 weeks old (Depending on outside temps)....HOWEVER I have an upside down laundry basket tacked to the back wall, at a very low level, so only the younger birds can scoot under it....Mainly they just ignore the little ones....once in a while a hen will peck at one that gets out of line, but usually there is peace in the coop.
Where are you going to brood your chicks? Can you make/build a LONG brooder that has hardware cloth dividers in it to separate the different sizes/ages? It seems you are going to have 3 ages....however you may find that you only have 2 sizes because the the breeds you have chosen. Use a red brooder light, it's more calming for the chicks and they can't see any blood, if someone does get evil and attack one of their brooder mates. Add new ANYTHING at night. No matter if you are adding to the brooder, the coop or the flock in general...do it at night when it is dark. (I have a hat with a light on it, it's wonderful for adding things in the dark....Father's day is coming, might want to put one on the wish list)
Roosters are wonderful. They will protect the flock...HA!!! They will ALERT the flock and alarm the flock if something isn't just right...."protect"? Not likely....they can outrun the hens and make it back to the coop faster. With that said, I have 3....two were raised as hatchmates and one was purchased as an adult. I don't have them for flock reasons I have them for breeding....I want fertile eggs so I can hatch my replacements. If you don't have a rooster a hen will step up and take over the "protection" role. BUT most people like the sound of a rooster, so I don't think you are going to have a problem with noise complaints. My neighbors missed my roosters crowing when I got rid of a bunch who were NASTY, before the new ones got old enough to crow. Most roosters don't crow all day.....Just when they want to be noticed.
Now about your building materials. 1x2 wire for the run? You won't be able to let the chicks out in the run until they can't fit through the holes and chickens are mainly feathers and can fit through smaller spaces then you would think. I had one hatchling fit through the hole in chicken wire, but couldn't find his way back to his Momma. Like I said "bird brains".
What predators did you say you might have to deal with? Coons? They will reach through and grab the neck of your birds and bite their heads off. EWWW!!! Possums too. How about rats? They eat eggs and chicks....one sneaks in through the wire and gets in the coop and sets up housekeeping. OK...I'm lieing, the birds will peck the heck out of the rat if they can, but he will steal your eggs and bite your chicks. (My chickens amuse themselves chasing the squirrels around the yard. And there is a dead one on the lawn....hope he died of natural causes) Snakes? They love chicks and eggs. Esp eggs. Are you doing to close your pop door (entrance from the coop to the run) every night? (FYI that gets OLD really really fast) If you build your run so nothing can get in (meaning hardware cloth instead of 1x2, at least on the bottom half) you don't have to make sure that the pop door is closed every night (365 days a year, 366 this year). Yes, it is more expensive, but how much is your time worth 365 days a year? Oh and planning your day to be home to close it before the predators sneak in. Did I meantion if you close it every night you have to OPEN it every morning? (I haven't closed my pop door yet. Well, ok, once or twice to catch a roo that ****** me off, but not regularly) And I strongly recommend you have an outside entrance to your run. I don't. It is my ONLY regret in my design....I can't get in the run to clean, retrieve mislaid eggs or add floor covering.
My first egg cost me $1200. (Not counting food) My coop has vinyl siding, however. I'm getting old and didn't need another building to paint every 5 - 8 years. The rest of the eggs were free. (again, not counting food) Compared to what my sister in law spends on photographing her kids (she has 8 right now) it's not as expensive a hobby as you might think. And what other hobby can you eat what pisses you off?
Definately get the Brahmas. You won't regret it. They lay wonderful eggs. And they are a big bird, so they won' t be tiny chicks.