Newbie needs help to set up tv streaming

[rodzer]

Hi guys,
I would like to stream two tv channels from home through a vps server that I would rent. I receive the channels from the satelite, and compress them by using my home PC, so that VPS would serve as the broadcast server.
I know how I can do this through the VLC player (broadcast option), but in this way I have no control over how many clients connect to the server at the same time, and this can cause jamming.
Which software do you suggest I should install on the VPS server to do what I described above?
Of course, I will create a website where the clients would log in.
If you can, please propose free or almost free solutions, as this is only an amateur playing.
Thanks