If you want to do all kinds of audio related stuff, you'll need a lot of different tools such as synthesizers, trackers, wave editors (like Audacity), and encoding tools.
Audacity is very nice and you'll need it for various small tasks like BGM loop mastering. I wrote a small tutorial about this btw: How to Create BGM Loops with Audacity
Also take a look at sfxr if you're interested in retro sfx:http://www.imitationpickles.org/ludum/2007/12/13/sfxr-sound-effects-for-all/
If you haven't done any music yet, check out some trackers. Tracker modules are pretty small and playback doesn't need much CPU, which makes 'em very suitable for downloadable games.http://en.wikipedia.org/wiki/List_of_audio_trackers
If tracking isn't your thing you can try some synth stuff. ReBirth2 is free
nowadays for example. It's not that powerful/flexible, but relatively easy to use.
Well, Rebirth is a pretty good starting point. Nowadays I'm using an outdated version of Orion
most of the time. Orion is rather cheap compared to other solutions... $99 for the Pro version and $199 for the Platinum one.
Of course there are also free synth thingies like Buzz
, but their interface is usually pretty awkward.