By the end of Book One of the hunger games we, the readers, can understand that Katniss' biggest challenge is

I think that would be President Snow and the government's vengeance for making them look weak in front of the population. They backed down when Katniss and Peeta threatened to eat the poisoned berries. This meant they did not have complete control over everything. Katniss will have to balance her newfound fame with President Snow's personal vendetta against her.

surviving >> survival

President Snow, keeping Peeta alive, not starving to death, etc.