Fonts are classified in many ways, but for our purposes, there’s just a few categories that you need to know:
Serif styles all have small ending strokes at the end of lines, and those lines provide a visual connection between the ends of words. Serif fonts have fallen out of style for screen use, because the screen resolutions are usually not high enough to show those little details properly. These really are the best for print books, and there’s a lot of sub-divisions that can be made here. If you want to really get into it, check out the PDFs I link in a previous post. It will have an effect on the emotional feel for your book, but that’s … another post.
Sans-serif fonts are best used in headings and display roles – when we’re talking about the print world. In the online world, sans-serif fonts work well for text … but if you’ve got the resolution of the real world, put it to use in your favor. Sans-serif fonts typically have an official feel to them, which will distance your readers from the text. Not what you want (usually).
Decorative fonts are those fonts that attract attention, are impossibly ornate, or are otherwise unsuitable for reading more than a word or two. That includes script fonts and those really ornate letters that replicate calligraphy. Use any font in this category for titles, but only on the title page. For a running head, you’ll want to put your book title in a Serif or Sans-serif font because it will be read frequently.
Fleurons are fonts (and elements of fonts) that aren’t letters or symbols; they’re a decorative drawing of some type. (Symbols are known as dingbats.) I’ve found many fonts that fit this description, and using them will really liven up a page – but you’ll need to make sure that you don’t go overboard, and that you fit the style of the decoration to the style of the text. Sometimes the text will be neutral, and you can use anything from Art Deco stylings to calligraphy flourishes without conflict, but other times… you’ll need to be careful.
Fonts can come from open source websites, from paid professional type foundries, and from hobbyists that release their efforts to the web. Be sure that you have the commercial license for your fonts, and that you have the italic face, as well as the regular (or Roman) version. (Although Rome is in Italy, so I’ve always found that nomenclature a little weird… because wouldn’t a Roman font also be italic?)
In any case, look at the links on my Resources page to get started, and you can spend way too much time deciding on what you really want. If you find that making the decision is a time-sink, make a decision between Libre Caslon, Libre Baskerville, and Fanwood fonts. They’re all open source, acceptable for book text, and that’ll get you started.