Ditto usna1985 advice, excellent source with great perspective.
We have a USNA sponsor son, History Honors major, who went Surface Warfare, then JAG via UVA Law School on the Navy's dime. That's not the usual way, as the Navy gets most of its JAGs through a direct commissioning program after they complete law school, or from those who serve, then separate from active duty, go to law school on their own dime or on VA benefits, then re-apply for a JAG commission. The LEP path from another warfare community is highly competitive. Many, many apply. Few are chosen.
I have an Engineering Duty Officer friend who did a 20 year Navy career, retired, went to law school, and is now with a law firm specializing in shipyard litigation. I have another friend, who retired as a Navy captain after 30 years, who went back to law school, and is now working for a major non-profit. There are all kinds of ways to take a journey with the law. I knew a lieutenant, USNA grad, submarine officer, who separated at the end of his obligated service, went to law school on VA benefits, applied for a commission as a JAG and to return to active duty, came back as a JAG, retired from active duty and now works for a defense contractor as in-house counsel.
Your son should be open to all majors and choose what he thinks he will enjoy, and let service selection take care of itself. The Surface Warfare community is arguably the more convenient platform for which to apply for the Navy's Law Education Program (LEP), but I have seen it done from many other warfare communities.
Search the forum for other threads on the Navy's Law Education Program, but here's a link to some of the Navy LEP info:
http://www.jag.navy.mil/careers/careers/opportunities_lep.html