Well the player is not really an issue. When I was broadcasting with JetCast, a long time ago, every media player was able to connect to the stream. The links on the page will need to be different though, as some media players don't use the same file extensions.
That is the playlist file that winamp will look for to play the stream. The port number, if set at default, will be 8000. You can always change it. When you click on the link it will open Winamp and start to play the file. I suggest not using Windows Media Player as there has been some problems with the streams opening correctly. Winamp would be the best one to use.
If you are using pictures then you can create a hyperlink within the picture that points to the playlist file. Most media players will use the .pls extension, and if they don't, Google will help you with figuring out what they are.
As for the dial-up and broadband choices, you will need to setup 2 streams that are playing the same thing. I would suggest using 24k for the dial-up stream, as I have noticed no problems with interruption. The broadband connection could be set much higher, but don't go too high. If you go too high, some people will have a hard time staying connected to it.