Oyster mushrooms are my favorite delicate mushroom that adds loads of flavor. They come in many colors, but most usual is a white or a white-grey color. The fresh ones have their caps down. The older they get, the caps start curling up. I love them steamed with kale. This mushroom must be cooked.
Mitake, also called hen in the woods (or, I guess, chicken of the forest) is a brown mushroom that you get more in a clump than individual mushrooms. In chinese medicine, it has medicinal qualities. When you get these, break them into sizable clumps, as they'll shrink with cooking. Adds lots of flavor. I'll guess it gets its name from looking like a cock's comb.
Last summer, I went to Phillip's mushroom museum in Chadds Ford, PA. Very interesting. Most of the packaged mushrooms here (I'm near Chadds Ford) and I believe in the US, come from Philips. Perhaps they have a web page, but I don't know it.
www.fungi.com is the web page for fungi perfecti, a place where you can mail order mushroom kits. Loads of info in their catalogue. I wouldn't recommend growing your own, though, unless you can put them out of your house--the spores get in the air and make breathing rough. I tried this for a few months in an apt, but went back to prepackaged mushrooms.