You are going to need a lot of blocks for this build so you should better get to farming. As for the blocks themselves, you can pretty much use anything. Cobblestone and Wood are the most common ...
Minecraft Tutorial - How to Create a Mob Trap and Item Collection Machine by drunkoncustard. Note that to speed up the process, this machine was created in Minecraft's Infdev mode.
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How to build a defense tower against zombies in Minecraft

Zombies in Minecraft might look slow, but when night falls or a raid begins, your base can get overwhelmed fast. Instead of constantly fighting them head-on, the smartest solution is building a proper ...