Getting ahead...

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

What do non-traditional career paths look like?

To be a hirable librarian, you need a master’s degree in library science and experience working in a library setting. As with anything else, the more experience you have, the more hirable you are.
As for ongoing training, different sub-specialties in the library field have different opportunities for continuing education and certification, but there are plenty of options in every field - anything from conferences and certificates to further degrees. Academic librarians often have an additional master’s degree in the subject they specialize in; law librarians will often have a juris doctorate, etc. More universal things are higher-level computer skills and web and graphic design ability.
As for non-traditional careers, there is a wide range of opportunities since librarians are experts at finding and organizing information. One of the more common non-traditional careers I've heard discussed is competitive intelligence research in business.