The Standard Infantry Rifle - it never jams, is perfect for long range, and is endorsed by the U.S. government in the fight against zombies.
Now, shameful references to a fantastic novel aside (and points for knowing the novel in question must be awarded, I feel) personally, I'd probably go for a machete. It's functional, doesn't need ammunition and is, most importantly, pretty cool, since, if zombies take over the world, surviving is gonna be damn difficult, so I'll go for looks and never mind the horrible and inevitiable death that awaits me one way or another.