You're better off buying a console.
$300-$400 budget, pre-built ( bad idea ), and you want to play Day Z and next gen games as well which is pretty impossible on this budget. It's not worth buying a pc with your budget and hoping to play current/next gen game as well. If you end up buying something around that price, chances are you're going to end up playing on the lowest setting possible or can't even run the game.
Sorry.