A four year degree is mandatory at any of the majors. Sure, some people will say you can get hired without, and sure, there are a few that have been, but the vast, vast majority of your competition will have it, and you don't want to give them any reason to toss your application to the bottom. Your degree should be fine, but conventional wisdom is to get one unrelated to aviation so as to have something to fall back on during the hard times (accounting, engineering, etc). And there are always hard times. US Majors don't care what your degree is in, and in fact, they like to see some diversity and interests outside of aviation.
Practically all of the US regionals operate jets of some kind. The majors don't care if it's a Airbus or a Embraer. The regionals don't care if you flew a Gulfstream or a DC-3. That your 1,500 hours is in a jet won't matter to anyone. There is zero chance to get on with the majors with that time, or even 3,000 hours for that matter.
Civilian track it is a LONG road to the US majors. Figure at least 6-7,000 hours total time, irrespective of the types flown (no one cares), including some good PIC time, a clean record and at least some instructor/checkairman time. That's 7-8 years of busting your tail.
Major US carriers simply do not care about type specific experience. Their point of view is that a good pilot is a well-rounded individual that has strong basic flying skills transferrable to any aircraft. They'll train you to fly their aircraft their way (and on their dime). Rather, they see the long period as a vetting process. If you survive the 8 years, most of which flying 121, and keep your nose clean, then you have a high probability of being OK, especially since all 121/135 training has a paper trail they review prior to hiring.
All US carriers, regional and majors, have a high expectation that you can manually handle airplanes PRIOR to showing up for training. The training is focused on systems and procedures with zero hand holding for basic flying skills. You are expected to have very strong hand flying instrument & flying skills from day 1.
Something relatively new in the hiring process over the last few years is that most US Majors want you to have some kind of community involvement...volunteering, interests outside of aviation, or similar.
Hope this isn't too discouraging.
Nu