Unfortunately, my question wasn't clear enough. (I'm having trouble getting my head around the logic of how WordPress deals with images, but I'm getting there.)
It isn't the thumbnails in posts and on the blog itself that I'm having trouble with. I think in Settings/Media, you control how those thumbnails look.
I'm talking about when you select an image from a gallery or the Media Library. The thumbnails there are 32 pixels by 32 pixels, and when pictures are similar, it's difficult to tell which is which. I have to click on "Show" for each one in order to see it larger. Then I get an image that is 128 pixels by 128 pixels. That is large enough, though still not ideal for my purposes. At this point, I'm choosing which image to insert into a post where, and I'd prefer to see the whole image (not just a part of it) and a somewhat larger image.
I've looked around for any settings that affect these thumbnails, but I can't find any.