Hey Policy24,
I'm a recent Georgetown SSP grad, so I may be biased. I'm also a mid-career government employee at the DoD and am looking at these boards again because I'm looking into the possibility of doing a PhD in Public Policy just for the heck of it.
All three of these programs are probably likely to get you to where you want to go, but SSP is the one I would recommend, for two main reasons: it will probably be more relevant from a curriculum perspective for the positions you described, and it's shorter than the other programs. I don't think it being a shorter program is a drawback in this instance, because SSP is probably the top program of its kind. Keep in mind though that government hiring officials (and most everyone else in government) are far less concerned with the rankings of programs than people on this board.
But like I said, all three of these programs would likely get you to where you want to go. Because you have an undergrad econ background, you may find that the public policy program has more econ-heavy options, but obviously SSP has better international relations and security studies courses.
As far as a law degree goes, that is far outside my area of expertise, but for what its worth, it seems like that would be an atypical fit for your career goals, and would take twice as long as SSP to complete. But may open up private-sector options that the other two degrees do not. I don't know anything about Georgetown Law grads' private sector job placement.