I recently got a student ticket at the MET.
It was $25, ususally at orchestra seat, available on the day of the performance. I went to the box office in the morning (they open at 10) to get the ticket for the evening performance, then I was told the student tickets are supposed to be on sale 2 hours before the performance. But anyway they gave me a ticket. I think you can get the best available seat at the time of purchase. For my case, I got the side seat around the 20th row, which was not bad. If you still wonder, you'd better call the Met box office.