Hi,
I store them with the onions and garlic to use over time. I might buy a few pounds as the farm season draws to a close. By the end of winter, I have a few left. They seem to have reasonable keeping power.
Some years ago, there was a long gone French restaurant in Highwood who made a sizeable annual purchase of shallots. They invited people to volunteer peeling them for few hours in exchange for a dinner. I have no idea what they did with those peeled shallots.
If you freeze them, I suggest double bagging them. I learned a few years ago, my youngest sister bought frozen onions. The next time I visited, I brought ten pounds of onions, which I chopped into various sizes and shapes. These were packed into freezer bags. Over time the odor crept into other foods stored in the freezer.
Regards,