Hi Brian,
The consideration of number of cells required for analysis and statistical significance is not unique to mass cytometry of course.
Dimensionality reduction and other complex (at least in my book) algorithms may obfuscate some of the core principals and statistical assumptions that should guide a rigorous comparison. If you wish to compare well defined or "canonical" populations, you may be best served by using conventional gating as your initial analysis step.
As Mike noted, the first thing to consider is the number of cells you expect to be able to measure in your populations of interest and the biological variability of these populations. These two quanta may be impractical to measure ahead of time, but you can use population studies to estimate your populations' frequency and generally applicable / acceptable methods to estimate biological variability.
For references on some high-level lineages see:
Intra-day and inter-day biological variations of peripheral blood lymphocytes.
Here.
Reference values for peripheral blood lymphocyte phenotypes applicable to the healthy adult population in Switzerland.
Here.
For consideration on applying biological variability to your measurement see:
Proposals for setting generally applicable quality goals solely based on biology.
Here.
If anyone else in the community would like to suggest additional resources that would be great!