For unknown population size, convenience sampling is preferable. This is best approach of non-probability sampling when you cannot proactively seek out subjects.
You will need to determine your sampling method before determining your sample size. That is because the precision of your estimates for each cluster, strata, or stage determines the overall accuracy of your estimations or comparisons. One you determine the units you will be sampling in the specific clusters, stratification, stage, etc., the sample size determination becomes much simpler as you can determine the sample size for each component and add them together.
I agree with James. The most simple sampling method is "simple random sampling with replacement" in which, in each selection of unit, all the population units have the same probability of being selected, 1/N. And each selection is independent of the others.