Very smart to convert a shed. If possible put in a second chicken door (so you can separate birds in the future, you will definitely use it!)
I just put a shelf under the roosts and scoop the poop up off the shelf into a bucket, when the bucket is full it goes into the garden (usually with some swet PDZ granules on the shelf). Benefit of using levels/shelves is that it maximizes the floor space. I penned off the area under the shelf and it serves as an indoor second hen house area roosters, chicks, injured birds or whomever else needs it (it has an chicken door leading to a separate outdoor pen).
As far as composting, I usually just dump the chicken poop right on my garden beds and let it slowly wash into the soil. It is a "hot" manure so you don't want to put fresh chicken poop near plant roots, but from my experience on top of the soil works fine, or mixed into the soil if you will plant the bed a few weeks later.