How do the sampling methods and sample sizes vary for the different types of quantitative and qualitative research?

Hypothetically, what sampling method would you use to conduct a study of your selected evidence-based practice problem/topic? Why?
How would you determine the sample type and size?

For my proposed PICOT question, I have chosen patient safety. (P) In a hospice facility,(I) how does lowering nurse to patient ration to 1:4, (C) compared to having nurse to patient ratio1:5, (O) help improve pain management and comfort measures, (T) in a 6-month period. This question is one I wonder how it will impact providing end of life care.