No.
And management/sanitation is much easier with few chickens in huge coop, and they are HAPPIER (behave in a more relaxed natural individual kind of way).
Six thumbs up to you; and please try to take with a grain of salt all the BYCers who are going to try to convince you that you "must" get more and more chickens til they are packed in to some mythical "rule of thumb" 4 sq ft per chicken. That is nonsense, they are much better off with a whole big lot more space than that, it's just a general idea of what you can get away with before risk of cannibalism gets too high.
That said, you may well want to section off part of the barn to use for other purposes, like storage or if you decide you want goats or turkeys or something.
As others have said, NO to chickenwire. You want something like hardwarecloth (galvanized welded 1/2 x 1/2" mesh) or galvanized 1x1" welded wire mesh, or even heavy gauge 2x4 welded wire mesh with something smaller-gauge added to the bottom 2-3'. You will need to SERIOUSLY DIGPROOF the edges of your run (you *are* going to make an outdoor run of some sort, yes, unless this is just a 3-sided shed rather than a fully enclosed barn?) and if the barn floor is dirt or gravel you will need to digproof its walls as well. I would recommend a 3' wide apron of 1x1 or 2x4 heavy-gauge welded wire mesh, attached very firmly to the foot of the run fence or barn wall and pinned down very well or covered with something heavy.
Surplus eggs can be eaten (you may find that just a dozen eggs a week is not enough once they're your OWN eggs), given to neighbors/relatives/coworkers, or sold to same (most states allow small numbers of homegrown eggs to be sold uninspected without problem; some states require them to be sold only on your property but others let you sell them at other venues; you would have to look it up. A temporary surplus of eggs can also be cooked and fed back to the chickens as a protein boost, which is good for them and they really like it)
Good luck, have fun, welcome to chickens
,
Pat