If your long-term goal is NRE, then the best and quickest way to get there is to enroll in college, get As in your intro technical courses, and apply for NUPOC NRE option as soon as you are eligible, which I think is toward the end of your sophomore year.
The Navy doesn't pay for your tuition to go to school in this route, but you do collect E6 pay plus BAH for up to two years until you graduate, which you can use any way you like, plus you are free to get a part time job if that's not enough.