I have an open-air coop, and I found that the rain blowing in is no big deal. I have a wide open front, windows on the sides, and upper windows, that are open all year, except for the cold months, then only the front is open, the other windows are closed. The hardware cloth screening blocks most of the rain. I've found, most of the time, the floor/bedding just gets damp. Now, if I get a hard blowing storm for hours, and the floor actually gets, what I would call, wet, the coop,because it is open-air (Like you are looking to do) drys out quick. I don't have to be running in and out of the coop, to open and shut windows, worrying about if it's going to rain or not.
Now as far as the floor goes. I have a raised coop, with a wood floor. I totally waterproofed my floor with a heavy coat of a rubberized roof coat product (Blackjack#57) that I got from Lowes. If I wanted to, I could take a hose and fill my coop with water to a depth of a couple of inches. My floor will never rot out, it's totally sealed and protected by the rubber coat. You are putting a new floor in your shed, get the roofcoat and you won't have to give a second thought to it.
Now as far as the floor goes. I have a raised coop, with a wood floor. I totally waterproofed my floor with a heavy coat of a rubberized roof coat product (Blackjack#57) that I got from Lowes. If I wanted to, I could take a hose and fill my coop with water to a depth of a couple of inches. My floor will never rot out, it's totally sealed and protected by the rubber coat. You are putting a new floor in your shed, get the roofcoat and you won't have to give a second thought to it.