Primary armament: Scooter handlebars.
People always get confused by this! Allow me to elaborate.
It's a set of handlebars from a foldup scooter, detached from the body. They're jagged but not hooked back, so they'll be able to break the skull but won't get caught so easily. They slide away to about the length of my forearm and extend to twice that, so they take less space to store. I can extend them just by swinging them, so it's not inconvenient. Aaaand they weigh about 1.4kg - not heavy, but with the length they can easily get the heft to break an arm, leg or head.
Secondary armament: A knife. A bladed weapon is multipurpose and this would likely not be used as armament much. The knife I have in mind is actually a military grade steel kukri; most of you would only recognize that from the Sniper in TF2 or from the Resident Evil movie/s, but they are in fact real. And a maglite torch (I have one).
As for other thoughts and supplies; a bag of Doritos and bottle of coke (shock food, ohgodzombiesnomgromnumhf) and aside from that eat on the go with whatever is available. Loot from homes, not stores, as every person instantly runs to the supermarket, and it will just get clogged and everyone inside will be chomped.
Carry supplies in my bag - it's not big, but I can comfortably carry 14kg in it at a brisk walk without any issues. So assuming they're traditional zombies, ie they're rotting and none too quick, I can easily triple their pace with a full load.
And also, portable music player. I can't concentrate without music, and it keeps me pumped so I can move quicker. Sure I might be a tiny bit less passively alert, so I just have to be actively alert (watch my surroundings, stay out of easy ambush locations when music is playing, etc.)
Page 3 + massive post because I enjoy thinking about zombie apocalypse/s way too much.