Have a look at what we use at https://fosdem.org [0][1]. In terms of software, a crucial component is voctomix [2], using it as a headless video mixer. Another invaluable component is nginx-rtmp [3] for streaming.

We made a heavy push to get all of this packaged in Debian. It's a surprisingly powerful combination.

[0] https://github.com/FOSDEM/infrastructure/tree/master/ansible... [1] https://github.com/FOSDEM/video/blob/master/instructions/FOS... [2] https://github.com/voc/voctomix [3] https://github.com/arut/nginx-rtmp-module/