Oh yeah, this is so murky.
Basically, the bare minimum you can give them is six megapixels - roughly 2000x3000 pixels in size. As long as the focus is excellent, that's big enough to print at any size.
However, by modern standards, 6MP is very small. So most clients, if you gave them 6MP files, would wonder why they are so small. In this modern age, you should usually be giving files of at least 10 megapixels.
Yes, this makes things even more confusing. You know, and I know, that megabytes are meaningless. As you say, if a photo has lots of white space or plain colour, its jpeg compression will be very effective, and the resultant file will be quite small. Is a 2MB file necessarily a bad thing? Of course not. But it's damned hard to convince a client of that, isn't it? Clients, especially male clients with small penises, expect much bigger file sizes.
I don't know, honestly. All you can tell them is the truth - that the file you've given them is suitable to be printed as big as a house if they wish, and that whatever dumb printer they've tried to use does not understand photographs.
I've talked about these issues a bit more in this article, and at length in the recent update to The Print Sharpening Class.