The most effective long-lasting weapon is one you can put together yourself.
Which is why I would like to suggest the humble Sock-Brick.
![Sock & Brick][http://wiki.godvillegame.com/images/c/ce/Hbs.jpg]
You're going to need to raid a shopping mall or clothing outlet for socks - should be easy since socks aren't high on the survival guide's most-wanted list. Strong socks are the best, so go for the tight-knit ones, or long winter stockings.
The accompanying brick should be easy enough to find in a dilapidated post-apocalyptic world. Just search for any broken-down building or construction site. In a pinch, any heavy object will do, even a common stone.
Then just tie the sock shut and swing it at offending zombies. Prepare a few in advance in case one tears. Keep extra socks in your supplies for this specific purpose.
And as an added bonus - you can also wear the socks.