Well all of your songs will be based on the Minor or Major scales, because those are the only chords that can be tonicized. However, if you want to get into atonal theory, then you could have a diminished chord be your tonic. I'm guessing though, that this kind of theory may be a little too advanced ( I don't even understand it that well ), so you could always write a song in a mode.

Example: Write a song in F Lydian

Scale - F G A B C D E F

Hope that helps