Definitely go with hardware cloth or 2x4 welded wire (not much more expensive than poultry netting). Some small predators will get through (or reach through the 2x4 size wire), so it's not as good, but much, much better than poultry wire.
The grass area will be all mud in about a month, unless you protect it. If you search this site for "grazing frames", you can see some examples people have done.
I would not spend money finishing the inside of the shed, other than a coat of paint. For the floor, some people recommend "Blackjack" coating instead of linoleum. Again, search for that and you can decide if it's a better option for you.
Roosts should be installed so that the 4" side is flat for them to sit on. Normal construction puts them on edge for strength, but you want the wider surface for the birds. Consider making the roosts removable or movable to facilitate access for cleaning. It depends on the location of the roosts as to whether that is needed, but easier to do if you think about it beforehand.
Read the invention thread here, lots of good ideas, especially for feeders and waterers. If I had your setup, I'd build a large feeder into the wall that would hold 50 lbs of feed. Give it a high lip so they don't waste feed (make them reach down far for the food).
Water may be best done outside, especially in the non-freezing months. Get electricity there if you can, for supplemental lighting (I use waterproof outdoor LED floodlights from
Amazon, and a digital timer from Harbor Freight). Also, if you have freezing in winter, you will want a heated dog water bowl for then. Plan the location and electric outlet while building, so all you have to do it buy and install it.