Ditch lotto. There's something about lotto they don't tell you until you get there: the last third of the seats are in the boxes, and technically partial view.
SRO is far better- it's cheaper, a great view, and if you get there early enough, guaranteed for you.
To get the tickets now, I would say get there about a half hour before they start taking names for the lottery.
"...everyone finally shut up, and the audience could enjoy the beginning of the Anatevka Pogram in peace."