It's best to think of them as two different adaptations of the same manga.
* Fullmetal Alchemist (2003) is the first anime adaptation, which deviates from the manga after a certain point.
* Fullmetal Alchemist: Brotherhood (2009) is a more faithful adaptation of the entire manga, telling a different story from the 2003 version.
So, you should start with *Fullmetal Alchemist: Brotherhood* from episode 1.