Right now, what I'm doing is playing around with fonts. I need to pick one to use for the main text of the book, but then in addition to that, I also need a font for chapter headings and subheadings. The object of the main-text font is to look professional and get out of the way. You go through your bookshelf, and look not at the words, but the font. If you never notice what font it is, that's a good sign. If you're remarking on the font choice in any way, it was a poor choice.
Look through the books on your shelf- or on your e-reader, whatever- and you'll notice some trends. The first thing you'll note is that the bulk of the fonts are serif fonts, meaning there are little hangy bits at the top and bottom edges of the letters. The font you're reading now is a serif font.
Sans serif, such as this font right here, does not have those hangy bits. They tend to get used only for quirkier works. More common fonts in books are things like Garamond, Minion, Georgia, New Baskervilles, Modern, or Palatino Linotype. (Times New Roman is common chiefly among self-publishers, and because of that, it's associated with amateur writing. So you might want to actually avoid that one if you ever get around to writing a book.)
That's the main text. The rules for chapter headings and subheadings work a little differently. You don't want to get too crazy, but you have significantly more license to be showy if you choose. The type here, by rule, is going to be larger and bolder, so as to say 'hey, we're starting a new section of the book now'. But you still don't want people to pay too much attention to the font. If you want to be showy, that's okay, but the font choice still needs to be appropriate for the subject matter. The wingdings fonts still aren't going to work, and neither are a large number of fonts that are only suitable for logos or, sometimes, nothing but the sake of making a font.
For one example of 'font for the sake of font', I bring you what is probably the most ill-conceived font I have ever seen, and one that should probably elicit no further comment: "God Hates Westboro". A font that parodies Westboro Baptist Church protest signs. That is... a significant amount of effort that must have taken to... do that.