Roughly at least, how many types of cells comprise human blood?
I think any answer to this question will be subjective, depending on what you consider to be distinct cell types --- how detailed the classification should be.

As you mentioned, if you consider all immune cell populations that can be separated by surface antigens, that's already a pretty large number. In 2013, the Immunological Genome (Immgen) project reported characterization of 249 immune cell types, and I think they are still working on expanding their catalogue (see immgen.org). One can argue about which of these are really different enough to be called "cell types", but I think it gives a pretty good ballpark number.

At some level of resolution though, the notion of "cell type" itself becomes slippery. While previously it was thought that many cell types were terminally differentiated (unable to change back to more primitive forms), we now increasingly find that these "cell types" are more like temporary "cell states", or phenotypes, that can change over time. For immune cells, this phenomenon is often called "plasticity"; for more information, see for example this paper. The advent of single-cell genomics has further strengthened this view, demonstrating that individual cells can dynamically change their gene expression pattens. These issues makes it hard to uniquely define and count cell types, and it might be more useful to reason quantitatively in terms of the phenotypes and behavior we can measure --- expression patterns, signalling molecules, metabolism and so on.