I can't speak to the process/criteria on the linguistics side, but so far the most encouraging feedback I have received from sociocultural faculty (1a/3i/0r/3?) concerns my statement and proposed project. To that end, I proposed a single project, with more detail than I initially believed I needed to provide, that spoke to something that I both have intimate familiarity with and that I was able to argue would benefit from ethnographic study and is currently politically and socially salient. I workshopped that statement for months and sent it to as many people as would read it for feedback, including faculty members at a few different programs - I wasn't shy about cold-emailing folks to chat and then requesting they take a look at what I had written, bc the worst that could happen is they would say no and you can imagine the best case scenario.
Otherwise, I provided a solid writing sample, had what I would describe as only "pretty decent" GRE scores (not great or even super good), and am a co-author on a single peer-reviewed article published in a professional public health journal. Also, I know my rec letters (3) were very helpful. I worked closely with each recommender to ensure that they cited specific examples of my work and experiences to support the flowery superlatives that is common across promising application packets and to make certain that it was clear that they knew me and understood my potential well.
Hope that is helpful, although I acknowledge that the exact same application packet may well have resulted in 6 rejections for me in a different year. For better/worse, luck seems to play more than a small role with these things. So, best of luck!