A spear being jabbed into a zombie head has a chance of getting stuck. Or if its a wooden shaft, of breaking when rammed into their skull. What then? If its just one zombie you had to deal with, your right-can make another spear fairly easy. If theres more then one though? Better have another weapon or be ready to run. And i think you may be underestimating how hard it would be to actually shove a spear into a skull. Theres also a chance you might not get a straight on hit, and end up only grazing the head.
Some good weapons and items id pick beside the crowbar would be a bow and arrows, a pistol, a baseball bat, a good axe, a hammer and a shovel.
Then the next best thing to do after picking up a bunch of weapons and food, would be to pick a good place to fortify as a safe home. So grab a bunch of planks and nails too.
But honestly if a zombie apocalypse did actually occur, it wouldn't be anything like the movies or games. For some reason people seem to forget a rather key detail about corpses-after being dead for a while your muscles atrophy, and eventually waste away. So most zombies wouldn't really be able to move. Only recently deceased ones could, and if action is taken quickly, you could easily kill a fresh zombie before it can act.