I can honestly say a kukri would be first and last on my list. Zombies first, anything else, last. Such an odd tool for generic use, but a great tool for cleaving flesh from bone or chopping. Also really odd to carry other than in your hand due to the curve.
I forgot I have a kukri. I picked it up at the Dale City Gun Show. It's called a Takedown, first production run, hand made in China. It's made from 1045 Surgical Steel. I think I paid $35 for it. It comes with a nylon sheath with three snaps on the back to hold the blade and a velcro holder for the hilt. This is not a fast draw sheath. It's got some heft to it, but I had issues cutting saplings with it.
In order of cost outlay from ~$40-$225-$525-$750:
Estwing Double Bit Axe-
Treeman Combat Machete-
Bugei Shobu Zukuri Wakazashi-
You might also consider having something custom forged for your precise size and needs, e.g. ask Sam Salvati here on MDS or the local boys at Baltimore Knife & Sword, who make some viscous tactical weaponry for a very fair price=> http://imakeswords.com/tactical.htm