Hi,
At Illinois Mycological Association, we had a mycologist named Betty Ivanovich who actively cultivated mushrooms. She grew mushrooms in her garden like many do flowers.
Her son had a business located near those two horse tracks on the southside. They grew oyster mushrooms in bundles of hay in yellow, pink, white and pearl grey tones.
They had mounds of horse manure composting outside. In the middle of summer or winter, there was steam rising from this pile. They used this for cultivating button mushrooms in old truck trailers.
I would be surprised if you could collect spores from supermarket mushrooms. Once they have been chilled, they tend not to drop spores any longer. If you want to try anyway, portabellas are mature cousins of the button mushroom.
We once had a club member who was developing a shiitake farm in Missouri. I bought a half dozen oak logs with innoculated with shiitake. If I kept up with wateriing, there was a regular flourish. A friend has an indoor pool, she kept her shiitake logs in there. She had shiitakes all year long, though they tasted like chlorine.
There are books on mushroom cultivation. The skill is replicating environmental conditions for the mycelium to thrive and occasionally sprout a mushroom.
Regards,