To answer to your question regarding the servers, usualy when you choose a broadcasting software you will get the feed from their server and the only thing you need to think about will be the traffic. Based on your traffic you can buy hosting packages which come with a speciffic amount of GB included.
It is not a performance problem here but bandwidth consumed in order to watch shows. If you have 300 users watching at the same time ,you use more bandwidth than when 200 are online at the same time.