Working backwards to answer the question, USNA grads who find themselves in the intelligence community, a restricted line community, got there because either (a) they were NPQ for a line warfare community and went straight to intel or (b) they went into a line warfare community, obtained their warfare pin, and applied for a lateral transfer into the intel community.
As for a major, the theory is that USNA equips you to serve in any community in the Navy or Marine Corps, regardless of major. You could be an aero engineering major, get NPQ'ed during 1/C year, and find yourself going to the Intel school pipeline -- and you would do just fine.
Intell officers do a lot of analysis, so being able to integrate qualitative and quantitative skills is key. A major that worked those parts of the brain, perhaps coupled with a language minor, would be a good combo. Intell officers pore over all kinds of data from intelligence sources, looking for patterns, trends, predictors. Can't tell you much more than that or they would shoot me.
The thread started with a question about a degree... everyone gets a B.S. out of USNA. There are a range of majors available --- see other threads for discussion on current policies on proportions of eng/sci majors vs. liberal arts. Again, a B.S. out of USNA gives you the baseline for every other school and occupation in USN and USMC.