In the very near future, humans (somehow) travel to a distant planet - and discover aliens who turn out to be uncannily like us. Their appearance is, to put it bluntly, freakish, but they are humanoid bipeds, and their life cycles, family structures, and basic needs are all reminiscent of human biology, albeit with the occasional surprising quirks. Their civilizations appear - at least at first glance - to have technologies, religions and political institutions analogous to bronze and late stone age cultures from the ancient Near East. It is not immediately obvious at first contact whether the differences run deep or are best said to be merely contingent.
Naturally, the very first thing the humans conclude is that these strange creatures are a veritable goldmine for the social sciences, and so they drop in teams of socio-cultural anthropologists (and perhaps also a scattering of psychologists, sociologists, economists, etc,) to do field research. The aliens prove very accommodating to all this... at least for now.
Given current academic practices, how do these anthropologists first go about it? Most especially, what are the major questions to ask, and models to test? What is the likely order of priorities, and what (aside from the blunt fact of meeting aliens, anxiety over whether contact is even desirable, and excitement no longer having only one species to study) is most likely to generate controversy or excitement?
Edited Note: I recognize that dropping in an "away team" is not wise or realistic, but take the question scenario as written.