Speaking from experience, go with the 1/2" foam board. I used 3/16 on the Barney cake in my photos and it was fine at first, but after it was moved a few times, the icing, and then the cake began to crack right down the middle. The cake board was just not sturdy enough for the weight of the cake once it was moved around.
For a single layer 12x18, a 3/16th inch foam core board (as the cake board and/or as the decorative board) will be fine......that said, I always put my cakes on their own 3/16th inch board the same size as the layer, so in effect, it's a doubled board directly under the cake.
HTH
Rae
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