Thank you. There are actually many mushrooms with gills or the fins you refer to that are delectably edible...in fact, of the thousands of mushroom species, only about 20 will actually kill you. For instance, the gilled mushrooms in the 3rd and 4th pic I posted are two of the most sought after edible mushrooms, the oyster and the golden chanterelle.
I would say that the best advice with mushrooms is to only eat what you are 100% sure of...and collect them with someone who is experienced when you are first learning. It is a fascinating world that can provide a lifetime of enjoyment, and is my absolute favorite excuse to go meandering about in the woods.