There are several thicknesses of cake boards available and depending on what sort of cake you are making will determine the size you need.
For fruit cakes and heavier decorated sponges I recommend a thick board or drum, as if not firm enough the icing on the cake may crack.
For lightweight cakes you can use the double thickness boards. Personally I like to display all decorated cakes on a drum board as makes them appear more imposing.
The thin boards are generally best used only for when you are stacking a tiered cake (one on top of the other). Put each cake on a thin board of the same size before iced and then stacked.
Types of Boards
Cake cards for Stacking