putting 24/7 live radio on website
Lithiumhosting is a great provider of streaming audio over the internet. They are pretty cheap too. I use their webservers and I am very pleased with their service!

As to what softwares you should use. It depends on how much money you are willing to put into it. A good way of doing it would be to use an analog mixing board and send the audio into the streaming computer. But you could as well do it on the computer. Again, it depends on how much money you are willing to put into it. Go to Google and study each software in depth. There are dozens of them.

Good luck!