Hm apparently the tree I had my eye on was black locust. I thought it was oak, but my neighbor knew because it turns out he planted it! He says he'll chop it up and I can carry it away. But I'm not sure whether I can cultivate mushrooms on black locust or not
This chart here shows several edible mushrooms and how well they can grow on certain kinds of wood but black locust is not listed.
It is hardwood though, so maybe it'll work.
@interneteh black walnut has a (possibly unearned) reputation for being somewhat toxic, at least to other plants.
@kewball yes, I have read that. I think the fact that the wood is seasoned somewhat will help