Well, as far as copyright goes, I'm quite certain you would need to contact the copyright owners for permission to use. This would include commercial music and retail FS2 music. You would be distributing someone elses music whenever you uploaded your MOD, and as such you would need permission to do so.
However, I do believe that small clips under a certain time length are legal. I have no source for this, nor can I really recall where I heard it, so research before you leap.
What confused me is whenever I hear remixes of commercial songs being distributed by people who I am certain did not contact the copyright holders... I'm not sure if there is some agreement or license that allows for this.
As for free-to-use music, search for "royalty-free" music. Good Luck!
Oh, and I'm preparing for this thread to be reduced into an arguement about copyright laws, whose right or wrong, along with plenty of people acting like they are legal gurus.