How to restrict access to the Internet?

Question

Squid

There is a server distributing the Internet. On it is a face with registration by SMS and through social networks. It is necessary that by default it does not let anywhere, except for this muzzle. And also to be allowed in social networks (vk, fb, ok) for registration through them, but only after pressing the “log in with @@@” button. How to implement it on the server than? Proxy? squid? If possible, not only tell the program, but also an approximate direction where to think. I don't ask for ready-made solutions. The correct message to Google (with keywords) is also welcome

Answer 1

If only search direction, then RADIUS

Answer 2

I googled such a thing as a captive portal (wifidog, chillspot, PacketFence, etc.)
Maybe it? Which one is better/easier?