Right now you need 1475 hours total time, and 25 hours ME to get hired at a regional. How you get it is up to you, CFI or 91/135. Both avenues provide good experience...
CFI's learn how to be in command in a "crew" environment, and learn some leadership/mentoring.
91/135 can offer some challenging experience and some of it has the added benefit that it will kill you if you suck.
Majors require thousands of hours of ME turbine experience, but you'll get that at the regional.