Do I need brackets for my wood countertops?

If your wood countertops were correctly designed, they should fit the underlying structure, like your hand fits a glove. In other words, it should lie right down on the support structure, and stay there without moving. Of course, this means it is a rather skilled practice to design and install wood countertops correctly, as they usually have legs that extend into the support structure, and they may have sealer material and trim, that also helps to secure them in place. Unless your countertop is radically missized, then you should not need any brackets, other than those that may link it to the substructure, which are planned anyway.