I started with uncovered (actually I started totally free ranging, but had to pressure wash all horizontal surfaces every week). Birds kept getting out. Turns out barred rocks have no trouble flying up 6 feet. Not such a big deal but we are getting ready to go away for a few days and I don't really want them out, so I get some bird netting from the HD garden department and covered the entire run (15 x 40 feet). Finally, only one was getting out. She was just skinny enough she could squeeze through the welded wire where one of the welds had broken. I put a layer of chicken wire over the bottom of the fence and now they are all in for a week.
I think you will want to go covered eventually.
Montyhp