question about networking for a noob

I am in south america and would like to hear advice on setting up a network. I would like to have one server that controls everything and have several monitors (6) connected. Each with keyboard and webcam, and mouse. All of the monitors are using just one program for web chatting so i don't see the need to buy 6 computers when all 6 users are using limited resources. is this even possible? one server with 6 monitors, keyboards, web cams, and mice running 6 of the same program simultaneously?