There isn't going to be one best answer for this kind of sampling. It depends on the observable covariates in your sampling frame, the variables you expect to be important determinants of survey response, and the analysis you want to run once the survey is complete.
With that said, there are a couple of general principles that can help guide your sampling strategy.
For descriptive surveys, you generally want your sample to closely resemble the population of interest in as many ways as possible. This will help keep your weights even, in order to maximize your effective sample size.
If you intend to do multivariate analysis, you may want to stratify on important variables of interest. This will increase variance in your IVs and DVs, and can help increase your statistical power in later analysis. This is why some studies conduct oversamples of minority populations -- because race and ethnicity are important IVs in many analyses. Case-control studies follow a similar logic for stratifying on the dependent variable.
If you intend to do description and analysis, then these are goals will be partly at odds. No matter what, you need to follow the basic principle of sampling and make sure that every individual in the population has a known, non-zero chance of being selected into the sample. Advanced topics worth looking up in this area include propensity scores, and sample weighting via raking.
Closing thought: these are general principles for sampling design and sample weighting. You don't say much about your specific application, but I'm guessing that most of this is overkill. The main reason to stratify a sample is if you have reason to believe a simple random sample will miss out on some important group of interest (geographic, demographic, or otherwise). That is, the sampled population would be too small for useful analysis. If you don't have that problem, then you don't need to worry too much about stratification.
A stratified design effectively means that separate surveys are designed within each stratum - units selected within one stratum are independent of all selections within other strata. Estimates of total are made within each stratum, and then combined to come up with the estimate of total across the population:
$$
\hat{Y} = \sum_{\text{strata}}\hat{Y}_{\text{stratum}}\\
= \sum_{\text{strata}}\sum_{\text{units}}y_iw_i
$$
The design weight for a unit in the survey should only weight the unit within the stratum that the unit belongs to. There is no need to modify design weights, assuming you have them.
I recommend reading Model Assisted Survey Sampling (Sarndel, Swenson, Wretman) or Practical Sampling Techniques (K Som)
Best Answer
Minimum sample size is useful once you consider that units might not respond. However, if you make it too large your design is going to be less efficient. If you aim for about $5$ reponding units should be enough. Bump this up with an assumed response rate $5/rr $. $30$ is more than enough - but will probably mean you are putting sample where it isn't needed for a good estimate of the total