It depends on the type of music your really looking for...
I have tons of experience with DAW software (Ableton, FL Studio, Reaper, Reason)
Through my experience I really love Ableton and FL Studio equally, thought they are paid programs.
Personally I like these...
Reaper: Good for just about any project, but I think it is good for more serious games
Audacity: Of course right? It is decent if you want to touch up things when your completely finished... DON'T USE IT TO MAKE THE TRACK LOL
PXTone: Created by the creator of "Cave Story". I find that it is good for chiptune style music.
Musagi: Also used for chiptune, but it is a good midi music software.
MilkyTracker: I have not used this one myself, but judging by the info about it you can create some pretty epic arcade sounding/chiptuney music in it.
Now personally if I were you, I would try looking for someone with more musical experience. Creating your own sounds can be difficult if you have no experience with synths, or VSTs. Don't let that discourage you by the way, we all started somewhere!
Best of luck to you

Anymore information needed just let me know!