What kind of quality is this stream going to be, if its anything good (bellow 400Kbps starts to look pretty crappy) then you'll need to be streaming it from a server with a lot of bandwidth.
That would be hard for your home PC to do unless you live in a data center. What you'll likely need to do is put shoutcast on a server and have your PC capture and upload to the shoutcast server, this is what shotcast is best at.
This way all you have to worry about is capturing and encoding that video on your home PC. With my capture setup: 2.4 Ghz AMD X2, 2048MB RAM and a standard SATA disk. I can capture and encode about 60fps at 640x480 with ffmpeg using the divx/xvid codec.
If this was streaming to a server and broadcasting real time I personaly would go for around 10-15fps @ 320x240. Means the PC is free to do other stuff while its streaming too, and it won't fall behind.
With shoutcast you can easily add a second stream for users that don't have enough bandwidth too.