You do need three instances running, but you can use the one server you have. Just make sure you have:
1. A separate config file for each setup.
2. Have 2 consequtive ports open for each stream, like 8000 and 8001 for stream type 1, 8010 and 8011 for stream type 2, etc. (It's not a good idea to pull them all together, but spacing to 10's works fine.)
3. Create separate shortcuts, running the shoutcast dnas with as parameter the config file for the stream type.
I use one server, to stream 5 different kinds of music, or even relay's, in this manner.
Last remark: It's all there in the example config file, so who don't you read it thourougly?
For you geocities link: Just use an anchor that leads to your stream (and port) on your webpage. You don't have access to ports other than 80 (http) on Geocities, unless you OWN geocities.