Well, before I give you my ideas, having read the book, what do you think the "big ideas" are? What struck you as you read this book about what its central themes are? What stood out to you? It would be much better for you to try to answer this question based on what your feelings about this book are rather than using other people's ideas.
Having said this, if you want three "big ideas," I would personally go for the struggle for survival, violence and the tyranny and control of the Capitol.
Throughout the novel, Katniss is shown to be a character that has to struggle to survive. In a sense, the Hunger Games are no different from her life before, and the grim struggle for her own survival and the survival of her sister and mother that she had to endure. This is what distinguishes Katniss from so many of the other tributes in the Hunger Games, as she has faced the battle for survival and won it so many times before.
Secondly, it is hard to ignore the theme of violence in the novel, especially as it is depicted as occurring between children. The Hunger Games, in a sense, form an apt metaphor for the kind of life that the citizens of the various districts enjoy. It is a dog-eat-dog world, where hardship and suffering are the norm. The only way to get ahead is by pushing somebody else down.
Lastly, the control of the Capitol is a key theme of the novel, as is the hatred that Katniss and others feel about it. Notions such as freedom are severely challenged in the wake of the power that the Capitol exerts over its people, and Katniss has to struggle hard to maintain her own sense of individual freedom and agency.