I do not have up to date info but I am sure Lourdes will contribute something soon.
A few years ago I was a guest of Monte dei Paschi and was seated in their personal grandstand above the mossa - more later. This was an unique experience as before the event we had a tour of their headquarters - we were only 4 of us - a Palazzo Salimbeni which seemed more like a museum rather than a bank!
The mossa is where the start takes place and it involves dropping a rope when all the horses are properly lined up. Until this actually occurs an hour may pass as the jockeys "jockey" for position which generally includes advancing to the rope at the last movement ensuring that the horse is moving forward when the rope drops. They seek every little advantage.
The only problem with the area of the mossa is that it is remains in the sun for most of the time.
This factor is important in determining from where you view the race as apart from the "mossa" time period there is that related to the procession of the various contrade and related flag throwing. So be prepared for a very long period seated and consider bathroom needs, sunscreen, hats, water etc.
But it is all worth it as it is truly a magical experience. The important thing however, is to remember that we are only guests of the people of Siena. This event has become a huge tourist attraction but for them it is so much more important.