There are two main types of pizza cutting boards, those made from wood and those made from plastic. Wooden pizza cutting boards are typically a lot nicer to look at but their plastic counterparts will be much easier for cleaning. A plastic pizza cutting board is typically dishwasher safe, whereas wooden ones are not and you must hand wash them.
That being said, over time, a plastic cutting board will get deep scratches and grooves and this is a flaw in the design since bacteria can hide in them.
A wooden pizza cutting board will be a lot more sturdy and this results in a much more durable product.
You should consider the cutting board material since there are several types of wood that are used for these boards. Hard woods are much better for cutting and serving pizza, they are more robust. Things like maple, oak, walnut and teak are particularly good.
However, there is also the bamboo cutting board. While bamboo is not technically wood and in fact, a species of grass, it is a very strong material.
If you do not have a pizza cutting board, you can just as easily use a cheese board or other type of chopping board. Your cheese board will normally be made from the same materials as a pizza board and can make a good alternative for food preparation, cutting and serving pizza.