Choosing within research design & methodology
Start from the kind of question you are asking. Questions about how much, how many, or whether one thing affects another usually call for a quantitative design, from surveys to experiments. Questions about experience, meaning or process call for a qualitative approach such as phenomenology, grounded theory, ethnography, case study or narrative inquiry. When you need both breadth and explanation, a mixed methods design integrates the two. When the aim is to improve a practice or a designed intervention while studying it, action research or design-based research fits.
Whichever design you choose, sampling and sample size need a justification: a power analysis for hypothesis testing, a precision calculation for surveys, or a reasoned argument based on information power for qualitative studies. Committees and funders increasingly reject rules of thumb, so the calculation is worth getting right early.