An ideal survival quote is found in chapter one when, during the reaping, Katniss thinks the following:
Anyway, Gale and I agree that if we have to choose between dying of hunger and a bullet in the head, the bullet would be much quicker.
Her sentiment alludes to the fact that those found guilty of a criminal act can be severely punished or executed. She and Gale have been hunting illegally and could easily have been discovered and would have had to face sanction or death, especially for being in possession of dangerous weapons. The reason they hunt is to ensure the survival of themselves and their families since many in District 12 have met this fate. The District is extremely poor and many die of starvation since resources are scarce.
Katniss met Gale whilst she was hunting. She learnt how to find food and to hunt from her father and, after his death in a mining accident, she was forced to find a way to feed her mother, her sister and herself. Her mother was supposed to have started working after his demise, but she was overwhelmed with grief and withdrew completely, not prepared to do anything at all.
Katniss was, therefore, compelled to find a way to ensure her family's survival. She was able to get more food than they needed from hunting and would then trade that for whatever else they needed and sell meat to the Peacekeepers. There was considerable risk in this since she was committing a criminal act. Those she sold to, including the Peacekeepers, kept silent since they benefited from her skill and were aware that they would not be able to relish the fresh meat that she and Gale provided if the two hunters were gone.
"Winning. It's not just having the arrows or outsmarting the Careers a few times, although those things help. Something happened when I was holding Rue's hand [...] Now I am determined to avenge her, to make her loss unforgettable, and I can only do that by winning and thereby making myself unforgettable" (242).
In this quote, Katniss equates survival and winning the Games to her ability to become "unforgettable;" Rue's cruel death has both inspired and challenged her to become a bolder player in the game. For Katniss, survival has become more than just hiding out and avoiding the Careers; she recognizes that truly to survive, she must play the Game to win.
"Gale and I were thrown together by a mutual need to survive. Peeta and I know the other's survival means our own death. How to you sidestep that?" (112)
This quote deals with Katniss' internal conflict over her feelings for Gale versus Peeta, but also brings in the aspect of survival as a commonality between the two. Survival in District 12 meant teamwork for Katniss and Gale, whereas in the Arena, Katniss feels like she must depend on herself for survival, making Peeta a definite conflict of interest.
Ummm, "Stay alive"?
Hey, that's what Haymitch says. :)
"Run and find water." Haymitch Albernaty