It's inevitable. The world will continue to improve until it reaches a breaking point. Technology will advance so far that humanity trusts it too much. Then an event, a linchpin, will occur that sets in motion the downfall of everything we've built. Whether it's nuclear war, a rise of machines, zombie apocalypse, whatever. The point is, preparation and the right team will be key when it all goes south. The right people, friends, allies will make the difference in a world that has destroyed itself. These would be my people...
1. Katniss Everdeen
Katniss rocks. Her bow is easy to replenish with ammunition because it can be found or made, the weapon is silent, and she has grown into quite the survivalist throughout the hunger games. Her skills include everything from tracking to hunting to garnering supplies, not to mention killing. She would be an invaluable team member to keeping the others alive.
Because Wolverine. The guy can heal, so he'd never need a medic, and he'd also be the bullet tank in any gun battle. No poison or radiation would take him out, and he could take ANYBODY. Those claws would cut through any zombie, robot, mutant or gang member the team came across.
3. Master Chief/ Cortana
The Halo games have proven that Master Chief is a force to be reckoned with. He's a combat and vehicle specialist, weapons expert in both human and alien weaponry, and has killed basically everything big and nasty that's ever threatened earth. You might argue that Cortana is a separate entity, but given that she spends most of her time in Master Chief's helmet, I'd say they're inseparable and a package deal. Therefore, Cortana would give the technological aspect to the team, hacking and controlling anything we'd ever need, not to mention providing valuable intel at every turn.
That's my team, and given the odds of survival with these experts, I'd say we're gonna survive the apocalypse a very long time...