It's quite flexible, really. My personal opinion is that the MPH won't really add a whole lot unless you go to a top school where you make good connections. If you're set on going into law, do a JD and develop a skill set on the side. That skill set could include journalism, research (more important), etc.
There are hundreds of JDs working in global health, though I really only know of a few off the top of my head. Here's one I know who's director of the NIH's Global Health Research Branch:
http://obssr.od.nih.gov/mHealth_Winter_2011/anand_bio.html
Here's another one who works at the Council of Foreign Relations and does a lot of writing/journalism/consulting related to global health policy:
http://www.cfr.org/experts/global-health-economics-international-law-trade/thomas-j-bollyky/b11198
Both of them went to Stanford Law School. With law school, I would say there's a greater importance on getting into a prestigious law school since the market is currently saturated with JDs. With med school, it's a different deal, in my opinion. It's not necessary to go to a top 5 law school as a global health lawyer, but it certainly helps considering the market is flooded with lawyers.
I've also seen JDs working at the WHO as legal officers (having to deal with international health law, etc). Salary varies. I would say anywhere from $60,000-$100,000. It really depends on where you work. In government, you'll make a lot more compared to academia, for instance. Those two people I listed, I don't know them personally, but my guess is that they pursued their interest in global health on the side (reading on the side, doing research on the side). The NIH lady, my guess is that an MD or PhD could have also taken that same position, but she had the skill set necessary for that position (the research experience). The JD is important, but you need to develop the global health skill set on the side. Get involved with research, do internships, make connections, etc, and make sure you actually need the JD for whatever you're looking into.
Lastly, see if international health law and global health policy interests you (does the type of stuff in this article interest you?
http://www.nejm.org/doi/full/10.1056/NEJMra1314094 )