The story picks up a few years after the Second Game. The second and first games put you in the shoes of Nathan Hale, the first human to survive being infected by the Chimera. He dies at the end of the second game, and you play as his sidekick Joe in Resistance 3. Earth has gone through a portal into a different star system, or even dimension maybe. The Chimera have overrun earth, and only a few people have survived in North America.
Begin with Resistance 3.