A walk-in structure is best if at all possible. At this time of year, garden sheds might be discounted at the big box stores, and they do work well, with added ventilation and hardware cloth covered window openings. You will want larger than you think!!!
At least four sq. ft. of floor space...
Most prefab coops are flimsy undersized and underventilated nightmares, sorry. Do post pictures, I hope before you are committed to it.
A garden shed conversion makes a lot more sense as a coop.
Mary
Welcome!
Crawling under a four ft. tall deck will get old very fast, and you will need to be there more often than you think. At least, consider using a shallow portion of the area only, so you can reach under the deck, not crawl far.
Your run needs some bedding, like bagged shavings, dry plant...