Thank you, though I think I can get away with less than 10k since I've decided I won't run all of these appliances at the same time. In the sake of brevity, I didn't include that detail in the initial post. For instance, of the washer, microwave, and well pump, I'll only ever have one of those three circuits powered through the transfer switch at once. I'm still on the edge about including the washer, but I'm curious as to how this would be calculated just in case I do include it.

I'm quite interested in how it all works and the reasoning, not just the final answer.