Everything depends on your research questions and purposes. With that said, the gold standard in quantitative research is randomized and of sufficient power for the sampling frame/population. Qualitative research varies, though small samples and homogeneous are common [purposive is often used, but qualitative can also be many kinds of samples]. Again, look beyond rules of thumb--think sampling frame and population.
Quantitative is about 'width' and numbers. This usually means a larger sample size or population with scaled questions. Qualitative is more about 'depth'. Hence it is about a smaller sample but using open ended questions to gain deeper and richer data. Both methods will be dependent on your objectives.
In quantitative research generally we go for Random sampling ( Probability sampling) and large sample. In Qualitative method we go for non probability sampling methjod, like purposive sampling, and small sample.