Both of those options are very strong duos and you will move along pretty smoothly.
One thing that's nice about necro/mage is this duo requires no gear investment to be effective. Since you two are new that's pretty sweet,
The shaman and monk are not only one of the best duos in the game, but together you form the core of an effective group for almost anything. Monks are exceptional tanks/dps, and shamans are exceptional healers if you take slow into account. If you ever get tired of duoing or want to grab more people to do something fun, it will be much easier for a shaman and monk to find something compatible.
Ultimately I would suggest you simply pick what you feel like you would enjoy, even if that means trekking your level 1 across the world to share that first kill.
Just a little tip if one of you decides to play the shaman: use the inner fire spell as a heal, it is incredibly efficient. With inner fire you're the best healer, even better than clerics, until 14 or so. If you sit down and only stand to cast inner fire between mana ticks, you can heal almost indefinitely at noob levels.
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