Anonymous wrote:OP here. And what if the mom is recovering from a c-section? Is the bris delayed or how would that work?
Even with a c-section, you and baby should be home within 4-5 days of the birth. Since the bris is held on the 8th day it is not an issue.
I have never been to a bris at a "venue," only in people's homes, and as a BTDT mom I think you will be much more comfortable at home. Note, also, that the mohel may prefer that you have a minyan for the bris. It is not required, though. But something to think about if you are only planning on having parents and grandparents.
Finally-- it sounds like you are not very religious and not super comfortable with the traditional ceremony of having a bris done at home by a mohel. There's no shame in that. Perhaps you would be better off with a hospital circumcision and then a naming ceremony later on. The nice thing about that is that you are not wedded to the 8th day. You can wait a few weeks or even a few months until you are back on your feet and ready to host a small gathering.