Getting ahead...

What is the best training for becoming a hirable millwright? What types of ongoing training or certifications are necessary to be an effective millwright?

What do non-traditional career paths look like?

It's my belief that the best training one can possess, as a millwright, is the ability to properly use rim and face and, more importantly, reverse dial indicating techniques to align a machinery coupling.
I know that everyone uses lasers now, but there is nothing that is more impressive to a prospective employer than for a millwright to demonstrate proficiency with the dial indicators. Anyone can use a laser, with a half hour's training. It takes a trained craftsperson to do it the old fashioned way.

I agree with Mark completely. Alignment procedures done with indicators is STILL the preferred method on most turbine decks. Also consider learning as much as you can about fluid power systems; both hydraulic AND pneumatic.