If the population of the clusters is very different then it will be difficult to meet your goal . See the attached. David Booth

Whoa David.  I don't think you can legally load that whole book. 

Cochran, 3rd ed., Victor, is the book that came to my mind first with regard to cluster sampling, which I immediately compared to another book which is much newer, Sampling, 3rd ed, 2012, by Steven K. Thompson, Wiley, and Thompson's book, which is very good, still has much less on cluster sampling than Cochran.  I have bought a number of statistics textbooks, mostly used, and the old Cochran(1977), or even an older version - though my 1st edition Cochran copy has less on modeling - is still very good.  I encourage you to obtain or borrow a legal copy. 

Victor, you seem to already have picked your clusters, based on some "specific criteria."  [I have used model-based ("prediction"/regression-based) sampling and inference, which can sometimes be done under limiting situations where potential bias is small compared to variance reduction that can be obtained, but it is highly unlikely that you are doing anything like that here.]  It sounds like you picked 12 clusters without a randomized selection.  You have a problem right there.  At first I thought you might be talking about how to select those 12 clusters, and was going to suggest Cochran, 1977, section 9A.3, "Selection with Unequal Probabilities with Replacement," with random probability of selection being the relative size of each cluster to the size of the population, which you could find other places, or better, without replacement, Section 9 A.6, or perhaps better of various choices, the Horvitz-Thompson estimator.  This would require you to census each cluster selected.  If you use multi-stage sampling, then after selecting your clusters in some randomized plan/design, you would sample again, within each cluster, by either the same, or some other randomized design.  This would get rather involved.

Regardless, you would usually assume bias is under control, though that may require some further study, and generally you use a variance estimate, and see what sample size will be needed to give you a standard error that you can live with.  When you have both number of clusters and cluster sizes (n and m) that can be an algebraic challenge, even if you can find or derive the appropriate variance estimate.  a jackknife or bootstrap might be helpful.  (Not my area.) 

(The reason I suggested unequal probability sampling is because you were concerned about the data distributions.)

Perhaps you did not mean clusters.  Perhaps you broke your population down into 12 categories which cover the entire population.  If you just need overall population results, then you could look up "stratified random sampling."  But if you need reliable results for each category, then you could treat each as it's own population, and use a sample design for each one. 

I have found that the Pennsylvania State University has some generally good information posted online.  You might look at the following, which has links at the bottom:

 https://onlinecourses.science.psu.edu/stat506/

It is for a class, but they make it available to all.  (I wrote and thanked them for that in the past, as I recall.)  I have pointed out parts of it to people on ResearchGate previously. 

Best wishes - Jim

Thanks David and Jim, you both have been very helpful and l have been able to calculate the sample size using stratified multistage sampling and Neyman allocation.

Neyman allocation for stratified random sampling within each of the 12 "clusters" purposively collected??? Maybe you need to ask your question again.

@james well it's not the whole book, it's out of copyright, Bill Cochran is dead, and you can find it on the internet. It also is about the only thing available on Sampling. Mea Maxima Culpa. David

Use Neyman Allocation