When you say "make," do you mean cutting and editing music that already exists, or do you mean composing and producing your own music from scratch?
For the former, I'd recommend Audacity, which is free, and not all that hard to use. A bit of advice: learn the hotkeys for zoom in, zoom out, and undo. That will make your workflow much easier and faster.
If you're looking to compose and produce original music... well, I recommend Reaper (which is not technically "free," but which has an unlimited free trial), and depending on what instruments you want to use I can recommend some decent free or cheap virtual instruments and effects.... but please understand that producing your own music -- while loads of fun -- has a steep learning curve, and is the sort of thing you can expect to spend months or years learning before you really get comfortable with it.
EDIT: As for the rules surrounding this:
As far as I'm aware, USAG's only rules are that it needs to be under a minute and a half and contain no words.
The legality of editing copyrighted recordings to use as routine music... I'm honestly not sure about.
But if it's illegal, I've certainly never heard of such a law actually being enforced.
As for whether it's legal to compose and produce your own music: that's certainly legal. The day it becomes illegal to write music is the day I riot with a banjo slung over my shoulder.