I have no idea how G.I bill works but it sounds like flight costs are not an issue for you. I wouldn't go through DCA. Try ATP or Ari-Ben Aviator down in Florida, they offer all multi-engine training and pretty much guaranteed job as a flight instructor. After that you will take your pick at the regionals and after a few years you can expect to apply to the majors, cargo, or fractionals.

Don't concentrate on being a pilot for the majors because you might find that you don't like passenger flying, you might find corporate or cargo flying appealing. Good luck and thanks for your service.