Narf, you'll be shot dead long before your sword or knives have the advantage. I'm not talking about some silly Zombie apocalypse, I'm talking about the real thing: somehow, someway, the end of modern civilization. The lights go out and STAY out! Then the gas stops flowing, the natural gas stops flowing, then we watch chaos begin to happen. No more grocery stores, or any stores, because no supplies are moving.
The REAL enemy is every other person not related to you.
Now you need to know how to survive, really survive: Catch food, defend yourself, make fire, make tools, heal/repair yourself, grow food, where to look for food, what to eat and what NOT to eat.
I'm with Pyro, bow and arrow will become the best weapon, eventually. Get the fuck out of the urban areas ASAP..better to do that before. Let the 1-10 Million people per city kill themselves off and use up their ammo doing it.
After that a firearm will actually draw attention to yourself and bring trouble, lots of it. Use only when absolutely necessary! Good idea to make/use a silencer when discharging a firearm.
Who has the best chance of surviving? Hollywood has it all wrong, it's certainly not going to be US office pukes, it's going to be people with proper RL training: Military and Police mostly.
Edit: oh and maybe some of us techy folks who know how to make bows and arrows and tools and basic medical facts, etc.
Good luck folks.