machete or sword is the best weapon, no maintenance, no reload, no ammo, no sound, just slice and dice and be stealthy, I'd have a sword like weapon, a shovel and a grenade for if it gets hairy, Get overrun, pull the pin and run at them yelling like tarzan kamikaze.
As for heading north, everyone who will survive the first few months will head either north or to the oceans so then you run the risk of encounter infected there. I'd head down, either sewer system or a cave like area where there is condensation for water and eat bats (a la Ozzy Osbourne

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One thing I learned from Call of duty and Left for dead, camping in one spot will attract thousands to you, you have run a continuous loop. Sewer system works since its like a network of streets so you just in circles. When you need supplies, hit the surface for some Dairy Queen
