Dave, I'm not sure if a camera is the right solution. I've been in training classes where all the students PCs could be pulled up on the instructors PC. If I had a question, the instructor would look at my screen remotely, solve my issue and even project my screen to the big screen if he thought others could learn from my mistakes. I can use chrome remote desktop to see my home PC from afar. I think Teamviewer might work, but pricey. I'm not an IT professional that can give you specifics about how you set permissions, how many PCs can be monitored at once, etc.
IMHO, a personal camera network setup in a classroom could be spun as inappropriate and lead to immense grief. I would encourage any solution to be sanctioned by the school's administration and implementation conducted by the IT department.
