I've never seen "Music Game", but it all depends on what you want to do. At the most basic level, you've got e-jay, where you drag+drop some previously recorded samples onto a score (you can also add your own sounds), and voila, you have a song.
If you want to record your band playing, or maybe just yourself, accompanied by some drums, a bass, whatever, then something like Voyetra, Kristal (free), or Audacity (free) would be good. They let you record from your soundcard several tracks, add basic effects, then you can arrange them how you wish. Accompanied by something like Hammerhead, a free drum machine, you could make some decent tracks using this setup.
To take things a bit further, you have Fruityloops, which is a sampler/sequencer/effects unit/mixer all in one, good to use with a midi controller, otherwise much the same as the above. Then there's Reason, Cubase, et al which cost a lot, and are probably best left until you've tried out some of the other (cheaper) stuff out there.
Hope this helps,
Rob.
