Textkit has inherited the broader problems in presenting Greek text on web pages. In the past, we used SPIonic, but now we use Unicode.
You will find SPIonic in older posts using Greek, and in a few of the Greek Tutorials, so you may want to install that font if you haven't already had a reason to do so.
Unfortunately, one past upgrade of the Forum software messed up all the Font tags, so you get to see unencoded SPIonic. This should always display completely, but isn't very nice to read. It is quite similar to Betacode.
Sensu stricto Unicode is not a font, but a method of encoding a writing system. It aims to provide a way to accurately represent every writing system in the world. Reasonably modern versions of all the major operating systems (Windows, Mac OSX, Linux and most Unices) will understand and correctly display any Unicode characters if there's a font available which can display the characters requested.
For Windows and Mac users (especially if your OS is pretty current), this presents no problems. Macs come by default with a Unicode font capable if displaying Classical Greek (also known as "polytonic" because of the many accent and breathing marks required). Windows users should see this Textkit post, which will explain both how to get the Microsoft fonts that can display polytonic Greek, as well as how to turn on methods to allow you to enter it.
Mac OSX has the concept of "Keyboard Layouts" which allow you to enter a dizzying array of languages. Versions 10.4 and later come with a built-in layout for polytonic Greek, but it's not very intuitive. Most of Textkit's Mac users use SophoKeys for entering Greek. That package comes with documentation explaining how to use the layout. If you're content to use Apple's, go into the "System Preferences" application, pick "International" and then the "Input Menu" tab. You'll want to check "Show input menu in menu bar", and then click the "Greek - Polytonic" layout. You'll have to log out and back in (or reboot) for this to take effect.
If you cannot produce Unicode Greek in the forum, please please please do not invent a new Latin transcription scheme for posting to the Forum. Often this is as hard to interpret as whatever question you might be asking. Please use Betacode. It's not very pretty, but it's unambiguous and widely used in scholarly circles for email, etc. It's also what SophoKeys uses, as well as this web tool which produces Greek for you: Greek Inputter.
If you don't like your system's default Greek font for Unicode, a list with examples can be found here. Of them, I'd recommend SIL Gentium as choice that is both attractive and free, though some do find it too heavy.