When you use a font in a static textfield, the font will automatically be embedded in the flashplayer. So you can use whatever font you want and it will always be seen correctly by the user, even if he hasn't got the font installed on his system. There are some fonts that will not be embedded by the player, but they are very rare. You can test this by choosing View > Antialias Text. If the font looks blurry, this means it will not be embedded by the player.
In static font you can also check 'use device fonts'. This means that a system font will be used on the users pc and not the font you meant it to be. Using this is quite safe for common fonts like courrier and arial, but not for uncommon fonts. In the top of your fonts list you'll find the fonts '_sans', '_serif' and '_typewriter'. These aren't really fonts, they're also device fonts. When you use these, the users system will use the appropriate system fonts. In most cases it's helvetica for sans, times for serif and courrier for typewriter, depending on which fonts the user has installed.
For dynamic and input text, the fonts are not embedded. You can embed them manually (using the charachter... button in mx) but embedding a font always means an increase of filesize.
The most common problem people have is they want a font to look crisp (aliased) but when you embed a font, it is anti-aliased an often looks very blurry. That's where pixel fonts come in. If you search the forum, you'll find a whole buch of sites where you can download them from. And if there's used in the proper way, they look crisp even when embedded.