If you're looking solely for those purposes, I think a Mac is ideal. You can get a dual processor G5 (1.8GHz) for $2000. There are also models for $2500 (Dual 2GHz) and $3000 (Dual 2.5GHz)
They all come with a DVD burner, but no monitor... they'll also come with all the software you really need: iMovie for editing, iDVD for creating DVDs and GarageBand, which will work for music, depending on what sort of "music editing" you want to do.