How do I rust proof a garage door track?
Carefully determine where the wheels of the bottom of your door stop being used.  Any point below the bottom of the wheels when the door is completely down should be safe to remove.  The track shouldn't have to go all the way to the ground.

I would not paint the track, for fear that it will interfere with smooth motion.  If anything I'd use grease to lube up the track, which will put a protective surface on the inside of the track where you need it and improve performance (less resistance).  

Rust on the outside of the track won't matter except aesthetically.