Is this enough support for my countertop?
We specialize in Countertop Supports. Using Hidden Brackets on the front base of your cabinet will be fine with an 18" overhang. We recommend you have no more than 4" unsupported countertop out beyond the extension of the bracket, meaning using a 14" plate/bracket would be sufficient. Also recommended is installing a plate/bracket at each end of the countertop within 4" from the edge, then spacing the additional brackets evenly between those two, 18" apart. I figure you would need 4 brackets.

For the 40" long, 38" deep countertop, I understand one side of this is connected to the countertop on top of a base cabinet. Are both ends of the 40"W/38"D countertop supported by base cabinets? If so, you can also use Hidden Brackets here as well. You would attach to the side of the cabinet base extending under the unsupported countertop. With the unsupported size of 40"x38", mounting to the sides of the cabinet bases, you can use 18" plates or 18" x 18" L Brackets. You would need to install 2 on each side of the cabinet base for a total of 4. You would place each 2 brackets within 4" from the edge of the countertop. This unsupported area would now be fully supported. 

If I have misunderstood your design, I apologize. If you could attach a sketch of your design, I will be happy to assist.