No matter how far you flee, a group of zombies will find you easily and make a meal out of you. Moreover, almost everyone will have to find zombie in the end, for which you will need weapons. The weapons you hoard should be of high quality and such that you can easily slay zombies with them. Apart from weapons you will also need intensive training to shed some zombie blood. Also remember the easiest way to kill zombies is to cut off their head or pierce their brain. So, you have to look for solid weapons with which you can smash a skull easily. Hammers will be a good idea and swords will come handy when you want to hack off a head. Also, a slim weapon with a smooth tapered point like a poker will be useful for a headshot.
http://talkingwalkingdead.com/survival-101-part-one-keep-calm-and-kill-zombies/