I think there was a discussion just like this a few weeks ago with some really good ideas; you might check there as well. I suggest that you choose events that build on Katniss' characterization and her relationships with other characters. Think in terms of what Collins' goal was to show you about Katniss through each event.
This depends some on whether you're going in order of how things are seen in the book or in the chronological order in which they happened. For chronological order, I'd start with the rebellion. Then I'd skip to the time when Katniss's father died. I would put in the time when Peeta gave her the burned bread. Then I'd say that when Katniss started hunting was a major event as well. From there, I'd skip to the reaping. How's that for a start?