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With 9 chooks, you will want a minimum of around 36 sq ft. So a 4 x 6 will not get it. A 4 x 8 would be a minimum space, and is the size of sheet goods such as OSB or plywood. Go tall with it ( 6ft min) for the sake of the chickens and their lungs/comfort. An airy coop with tons of ventilation at the top above the roosting ht is desirable. Should be open year-round up there, like mine is. Cleaner air for them to breathe and stays drier too.
Definitely do a bumpout for nest boxes on this small of a coop. You only need 3 nests, max. Trust me. Use the other space in the bumpout for storage of necessities such as a poop board scraper, feed, calcium supplement, etc.
Still, sounds like you should look into grandpa's idea of converting an inside space, provided the outside space adjacent to the building in question has suitable space for a run. Regards a run, do not use chicken wire because nearly any predator can tear through it. Do allow a bare minimum of 10 sq ft/chook or 90 sq ft bare minimum. I allowed 80 sq ft per chook for mine.
Plan to build the roost pole 12" from wall and plan to put a poop board 24" wide under it. Make it at half the ht of the roost so they can just use the poop board to hop up to the roost. Make the poop board removable and make it of 1/2" OSB and glue linoleum on top. Mine just sits on 2 arms. Scrape it daily
to keep your coop from being stinky and you will find that litter only needs changing once or twice a year.