Your webhost/external server would need to support running Java Web-applications in order for you to be able to run subsonic. As well, all of your music would need to be accessible by the server that subsonic was running on.
A quick look at the following link (
http://www.networksolutions.com/web-hos ... on-alt.jsp) tells me you would need the Pro level of hosting from network solutions in order to run subsonic.
If you google for "Java servlet web hosting" you might find something cheaper. The main point is that you need to be able to deploy a .war file.
Additionally, you may have trouble as Subsonic seems to want to keep it's database and other info in places like c:/subsonic or /usr/var/subsonic, and I am not sure if that is changeable.
- Munky