My time slot is 11:00 AM on Tuesday, April 29. I can buy up to 5 tickets then, if any are still available. They have divided Nats Park up into 5 "zones" and you buy 1-5 tickets in a zone. Then you don't learn your actual seat assignments until a week before the game. Tickets range from $40 (uppermost parts of the upper deck) to $175 (PNC Diamond Club) each.
I have bought MLB Playoff tickets at two different ballparks during deep playoff runs and getting Bananas tickets is way more complicated than that.