I've seen a lot of people referring to "1st boss", "2nd boss", etc. As far as I can tell, that's more common than calling them by their name, and most people seem to understand it. As I haven't really had time to play it all that successfully, I've yet to meet a boss, too.
Is there a fixed order, or some kind of suggested order in which one should pursue the bosses? Can I influence which boss I'm fighting next?