It must be easy to add ingredients into, so if you have several different sizes of bio-matter, you should account for that in creating the door. You should put the compost into a container that is closed off completely, other than some air holes (we're dealing with living organisms here and the heat must vent off as well a bit). The only exception is the door, so you can put more waste in it. Make sure the door has a latch or a way to secure it tightly. Small animals like cats will try to pry open the door to get to the food inside. Make sure it's tamper proof.
Your container shouldn't be flat or hard to turn. Cylindrical is best because you will need to mix up the ingredients in much the same fashion people cook a pig or lamb over an open flame. You will be turning the compost bin and shaking things up inside. Think of it as providing travel for the organisms so they can more readily, quickly, and efficiently continue to get fresh food to consume and process into useful soil food.
Optimally, to continue with the "green" theme, a container made of renewable or recycled material is best. Avoid using pressure treated lumber. The reason is this material contains toxic chemicals used to treat the wood that will kill your compost organisms and further this could contaminate anything you use the compost in!
Air circulation is required. There are a lot of processes going on inside the composter and you will need to allow the smells to vent out to avoid suffocating the microbes and other detriments to the organisms.
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