I think you can get there through both channels. I would decide based on what you want, as I personally don't like corporate flying. However, I have heard that if you want to get a job for a 121 carrier, doing a job that most resembles that job would probably be best. This of course would be a 121 regional that is flying in the colors of a major. You also generally fly more at a regional, although the upgrade time may take longer. Of course, these days the majors may not be hiring for awhile, so my best suggestion would be to go somewhere you wouldn't mind staying for a few years. Hope this helps you.
I've doen both (American Eagle, Midway and EJA) and it does depend on what you like. Personally, I loved the airlines but I also love corporate as well because you get to interact with people on a regular basis and not just cattle hauling. Plus, EJA gives you the best of both worlds: It's corporate with an airline type enviroment. Training is as good or better than anything I got in the airlines and the airplanes are 1st class!!! Don't EVER have to worry about writting and airplane up and getting 'red carpted' to the CP's office!!! At some regioanls you are expected to carry 'floating write-up'.....not here. And the list goes on. EJA is certinally a 1st class operation. No IF's, AND or BUTTS.
As far as getting to the majors - either will get you there. The real difference is quality of life. If the truth be know - I don't know if I will leave EJA now that I'm here. The majors would be great but its not longer a "must" now that I'm at EJA. I don't think most people at the regionals can say the same thing.