Veteran Seeking Advice on Career Path

Hi, I‘m a Navy veteran in my late 20s and go to Baruch studying for accounting, currently holding a 3.5+ GPA. I've heard that Baruch is not so famous outside New York, but has a decent reputation within the city, and Big 4 is probably the best offer you can get as an accounting student after graduation. But I'm really interested in working in IBs. I'm that type of person really likes challenge and willing to give up all my time to achieve my goal. I think the value system of investment banking perfectly fits me compared to not so exciting jobs in accounting firms.
so here are some of my career plans towards investment banking and I need suggestions from people with experiences.
Should I get a job at Big 4 for a few years then get a degree in MBA and make a turn around into IBs
or go straight for IB internships and take a shot at a full time position?
I also found that big investment banks such as Goldman, Morgan and Deutsche have a special job pipeline called Veteran Integration Program(VIP) which exclusively train and hire veterans into job positions in their firms but its extremely competitive and selective. Can any of my military people give more information about this?
Responses are greatly appreciated.