'try my best' is more or less a synonym of 'do my best'. Obviously, 'try' and 'do' have different meanings, but in the context of this particular phrase, I think that they amount to the same thing.
Neither of the other two phrases are quite right, I'm afraid. Two other possible phrases come to mind:
'do my utmost' - this is quite a formal phrase
'give 100%' - this is an informal expression