People love to play with fonts once they get their hands on a machine full of them, and often end up making quite attrocious looking documents. There's a very simple rule; keep it as simple as possible. Don't use a multitude of size, style, or colour changes; or any other multitudes of different things throughout a document. A good rule of thumb is to make all the body text the same, do the headings a bit differently, and think carefully how you might want to emphasise some sections (italicise it, draw a box around it, etc.).
A very long period of study has come to the conclusion that for machine produced text (very regularly printed text, unlike handwriting), fonts with serifs are easiest to read (Roman style fonts). The serifs break up the jumble of vertical and horizontal lines that form the letters. So it's traditional, and practical, to use a simple serif font for the body text. There are a number of serif style fonts which have been designed for ease of reading, most word processors are set to use one of them by default—a “Times” font is the usual one. I prefer Georgia, though it's a bit bolder (so it'll use more ink). And our old World Book Encyclopædias used Baskerville, which is lighter (less bold), simple and quite pleasant looking (it had an article on why they chose it, not too dissimilar from the information presented in this one—it was chosen for ease of reading).
This leaves you with a simple solution for making your headings and captions stand out; use a sans-serif font for them, and it's probably a good idea to make them bigger and bolder. Heading and captions are usually short enough that people don't have to read a lot of characters printed that way, and they're often larger than the rest of the body text. So the increased difficulty of reading sans-serif isn't too significant. You could use a much fancier font for headings than usual, but that harms readability, and generally looks silly.
Now you have to consider how you might want to emphasise certain words in parts of a document. For them, it's better to make just a slight variation on what's around them. It's usual to use italics to emphasise something, and when using a foreign word in the middle of a sentence. It's also usual to avoid using bold text unless something needs serious attention drawn to it. Underlining is best left for headings, if you must.
If you need to emphasis a block of text (such as a set of examples, or a quoted reference), then it can be better to emphasis the block rather than the text within it: Draw a box around it, indent the whole block, etc.
For the main body text, legibility ought to be the prime criteria for most works. It's better to restrict your artistic wants towards titles, and other small bodies of text. As already mentioned, serifs help with legibility, but it's only part of the equation. A combination of factors makes text easy to read, such as:
It only takes a small variation on any one of those factors to make a significant difference to legibility. For example, only a small variation in font sizing (e.g. just the difference between ten and twelve point) can make a big difference in how fast you can comfortably read the text (being too big can be just as bad as being too small). But changing yet another one of the other factors, as well the font size, can make it easier to read, again. There isn't one best answer for each of them, it's the right combination of all of them, in a given situation, that makes something easy to read.
For instance, some factors might be out of your control, such as a low resolution medium (e.g. an inkjet printer) might require bigger text to aid legibility. Given a better printing system, a smaller font might have been easier to read. But because you've got a limitation, you might want to adjust several of the other parameters to compensate.
I find that Georgia is good for reading on-screen (it's weight and aspect ratio suit me fine), but it's bolder than neccessary when printing (uses more ink, and looks a bit too heavy). Baskerville prints rather nicely on paper, but looks a bit of a mess on the screen (it's too light/thin for decent rendering on a low resolution medium, which all screens are). And I find the usual Roman font, “Times New Roman”, on Windows isn't a particularly good looking Roman style font. All of that boils down to a couple of things: Use the font best suited for the task your documents are really intended for (printing or reading on screen), and do a small test print with a few paragraphs using different fonts so you can see that what you eventually print out looks nice (don't be overly concerned about how the document is previewed on-screen while you type it, it's the end-result that matters).
You can often increase the repertoire of fonts on your computer by updating a Microsoft web browser (the updates usually have an option for adding more fonts), or installing/updating a word processor (they often include quite a few fonts). And there's plenty of places on the internet to get free fonts, or buy fonts from.
I've seen various nice fonts on Linux systems, though I haven't come to any conclusions about what's really good looking, and I don't know what's commonly installed on different distributions. I'm not familiar with the Mac, nor the fonts available to them. But the same advice applies: What you see on the screen and on the page aren't going to be identical, you should do some tests.