Tough question. I'm assuming that it's most likely inappropriate to simply point to one of my own studies.
I think the decision to choose an article needs to be based on a series of principles: a study that demonstrates a (at least one) purpose of Applied Linguistics research. This in itself is difficult because AL is so broad in its scope. I'm interested in language learning and teaching, but AL studies also include analyses of power relationships, and such esoteric investigations as the use of 'r' in 'fourth floor' in New York shopping centers to show social status. For each of these different purposes, the methods and approaches for conducting a study differ. However, one fairly consistent element is the collection of data from participants who are actually using the language. So classroom studies that collect data from classrooms, or power studies which collect newspaper reports which marginalize a particular group, or recordings of people saying 'fourth floor' in New York shopping centers are going to be useful examples of AL research.
I think if I can choose just one, I'll go for Fiona Copland's study on face in feedback conferences. It covers aspect of face and politeness, and power between trainers and trainees in a language teacher training context. It even discusses a communicative purpose of laughter. The perfect example of an AL study.
https://publications.aston.ac.uk/id/epr ... isions.pdf