One of the easiest ways is to use a Shoutcast service on your network and stream from the local network, but with your internet bandwidth capabilities you will max everything out very quickly, not just your stream but all the other traffic on your network. If you can find anyone with Linux experience IceCast is a free and very stable media server, providing you have control of the available bandwidth.
Some companies will provide free streaming, the downside is you lose a certain amount of control and they sometimes put in weird advertising and keep your archived content in formats that are not standardized. Beware of having your audio put into a codec format you do not 100% understand.
For a more scalable and robust solution, you might try a hosted "relay" service where the station provides a single stream to a streaming server mount point at a data centre located on the Internet backbone. When someone wants to listen to your stream, they will connect to it via this hosted service.
This way you can have as many listeners on your stream without costing significant bandwidth or disruptions. The other advantage, is depending on your service agreement, you may have it setup so that you only are charged by the actual listener(s), rather than a flat fee assuming you will have thousands of listeners all the time.
How you get your stream to the relay point depends on the provider, but most will accept a generic stream from Shoutcast/Icecast. Some providers will supply a software encoder while the most stable implementation is to use a dedicated hardware based encoder that are only a few hundred dollars and consume little power and don't crash like a PC.
To attract stations and customers to streaming service providers, companies will bundles other services like detailed reports and intro streams and embedded flash players. Its easy to search out and find companies that provide streaming services. Caveat Emptor.