I'll try to tackle everything one at a time. Everyone has their own opinions on most of the issues you've raised, so I'll give my own.
First off, all you need is some CD burning software. Adaptec Easy CD Creator is the most popular package, followed by Nero.
Some people find Easy CD Creator to be buggy, but I've never had a problem with it. Nero doesn't has as friendly an interface, but is more configurable than Easy CD Creator. For the things you'll be doing, I'd probably say Easy CD Creator is what you want to use, since you'd probably never touch the advanced features of Nero, and could possibly have problems finding your way around it's interface.
What else can you burn?
You can make music CDs that you can listen to in an audio CD player.
You can make backups of your data.
You can burn large amounts of data, that wouldn't fit on a floppy or Zip disk, for use on someone else's computer.
You can make a PhotoCD (basically, a CD photo album).
You can make a CD-Extra, which combines data and audio on the same disc.
You really don't have too many limits on what you can do with it.
Helpful Hints?
I would say the best advice you'll get is to read through
http://www.cdrfaq.org/. It really is the best collection of information, and explains everything very clearly, from the basics to the advanced.
Where to download songs?
Since the demise of Napster, which I didn't like that much to begin with, a lot of people are asking this question.
My favorite source for music is Usenet, which you should have access to via your ISP. Specifically, the group alt.binaries.sounds.mp3 has the widest array of songs. To access it, you'll need any basic newsreader application. Outlook Express has a news component built-in, but it's not very good for binary downloads. I recommend Free Agent for a basic newsreader.
The downside is that it's not a collection. You can't just search for a song and find it.
It's simply a binary newsgroup, so the songs available are only those that others post. However, they do have a requests group in place, and many of the users are excellent about fulfilling requests.
Hope this did well to cover the basics. If you have more in-depth questions, feel free to ask. I really recommend reading that FAQ though, since it will probably answer 95% of your questions.
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