Put up a solid wall wall between the chickens and your storage. You'll be surprised at how much dust they generate. A lot of that dust is powdered chicken poop. A door between the two sections would be nice, but the dust is real.
A photo from outside with an overall view might help. General size could help too, but I can get generic. In South Carolina you will need a lot of ventilation. Heat can be a killer. You also need ventilation in the winter to get rid of the moisture and ammonia, but the summer heat is your biggest concern in South Carolina.
Depending in what your roof looks like, you can maybe take out the top 6" of some or all your walls and cover that opening with hardware cloth. You can also or either do roof and gable vents. These openings should be over the chickens' heads when they are roosting and should be open all year long. It's practically impossible to have too much ventilation over their heads, even in much colder climates than yours.
In the summer, you need other ventilation down low, at least as low as where they are sleeping and preferably even lower. You can accomplish this by cutting openings and covering them with hardware cloth. Predators can climb in so whether you install a regular window or just frame out a hole, you still need to cover that opening with hardware cloth. If you just frame out and cover it with hardware cloth, you can cover that with a sheet of plexiglas or something similar in the winter if you need to.
Ventilation really is important.
You'll need a way for them to get to the run. I'd suggest a pop door, maybe 12" square, with the bottom of this opening about a foot off the floor. This gives you room for bedding without it falling out. They will have no problems going up that foot to get out or in, but if you wish you can put a cinder block there to act as a step. You can either do a guillotine type door or just build one with hinges. Either type shoud have a hasp so you can lock it.
I don't know how many chickens you are planning on or the sizes of the coop portion, but put a roost or two across it. Make the roosts higher than anything else you don't want them roosting on or in, like the nests. You'll need at least 8" per chicken on the roost but I suggest being generous with this space. Mine get meanest toward each other on the roosts while settling down to sleep, especially if I have younger birds in the flock. I find it helpful for them to have some room to spread out if they need to. With roost space or just general coop space, I find it best to provide extra room instead of trying to cram as many as you can into a space.
I'm not sure of this is the type of stuff you are looking for. Good luck!