NP for Missionary

I would say FNP hands down so you can care for people across the lifespan.

You may have an easier time doing missionary work as an RN than as an NP. Some programs will not accept NPs or PAs because they have to have supervision by an MD, which can create issues if MDs prefer not to supervise. There are also issues with international recognition of NP licensure; in most low-income countries the NP concept doesn't exist, therefore it isn't recognized and regulated which can consequently inhibit practice. It seems like several organizations are coming around and making it work (i.e. Doctors without Borders), but you may encounter more roadblocks as an NP than as an RN or MD.

It does seem as though there are particular higher-need areas, including anesthesia and nurse-midwifery. Here's the Doctors without Borders page for RNs and NPs (notably, PAs still can't work for Doctors without Borders for the reasons given above):

Registered Nurses / Nurse Practitioners | MSF USA