There are many opportunities. The first thing I would consider in your case is the Naval Academy. If you can get an appointment slot, not only would your education be free, but you would be earning a paycheck while you were getting your education and would become an officer directly upon graduation. (https://www.usna.edu/Admissions/Steps-for-Admission/index.php)
The next option would be a Naval Reserve Officer Training Corps (NROTC) scholarship. The programs will be slightly differrent depending on which school you attend, but there are many colleges throughout the US with NROTC programs. (http://www.nrotc.navy.mil/scholarship_benefits.html) You can either get your NROTC scholarship first, or you can begin college and attend the NROTC program as a volunteer and apply for the scholarship at a later date, but you would then have to find money for your initial classes.
Finally, you can do what I did, which was to enlist immediately after high school. I originally intended to do my 4 year enlistment and use the GI bill to fund college, but I was picked up from active duty for a NROTC scholarship. That program has become the Seaman to Admiral program, or STA-21 which selects high performing sailors for college and commissions as Officers.