What careers are superlative in the navy to get promoted to ranks such as captain and higher?

I want to join the navy after i finish my associates degree, I no i need a bachelor degree to become a officer, but i want to serve three years as a non-commission officer before excepting the duties as a leader. The second reason is the navy pays for your college after you serve three years. So my question is what career are best for me to get into to have the potential to become a high ranking officer? Thank you for the answers!