I think the theme of protector is prevalent throught the book. Katniss first steps up to protect Prim, Peeta protects Katniss in the arena, Cinna protects Katniss's image, Haymitch protects Kat and Peeta in the arena and so forth.
Ironically, many of the roles of protection switch during the course of the series.
What of the genetically engineered wasps? Is the author's use of Roman names for characters in District 1 symbolic? Isn't each district symbolised by something?
IE Find your own - symbols are not fixed; they tend to be configured by readers.
Another concept you might like to explore is that of the metonym.
I would suggest that Katniss' bow is a symbol. Her bow gives her strength. Whenever Katniss has her bow, she is invincible.
Outside of that, the games themselves represent oppression. As seen in later novels of the series, the games are questioned based upon the oppression they place on the tributes and the districts alike.
As for my team? Go Peeta!