One option is to keep a Windows partition on your hard drive and use Wine to run your Windows applications under Linux.
To get Wine you'll probably want to use Automatix (www.getatomatix.com) - and the cool thing about that is you can get all of stuff you need to play multimedia files, the latest version of Firefox, Java, Flash and a whole bunch of other nifty stuff Ubuntu can't legally include on the CD.
Searching Synaptic (the program that Ubuntu uses to automatically download and install programs) for "music notation" will bring up a short list of programs you can easily install. If you search around SourceForge, Freshmeat and a few other sites you will find a long list of programs you can try out.
As for your network connection, it should "just work", Try out the LiveCD option and see what happens. If you have problems, check out the forums on the Ubuntu web site.