Regardless of whether you use Windows, Linux, or Mac, the first answer to this question is that you should not be using a font that replaces Latin letters with the shapes of Greek letters (which typifies fonts created in the 1980s and 1990s). Rather, you should type all Latin, Greek, Hebrew, Russian, Chinese, etc. using.
The advantages of this approach include:
Unfortunately, the most popular font on most systems is Times New Roman which, while it does include modern Greek Unicode codepoints in its range, does not always support the many polytonic accents necessary for writing and displaying ancient Greek (it depends upon the font version). However, at least three of the other most common (and attractive) fonts from the Microsoft packages do support polytonic Greek: namely, Palatino Linotype, Arial Unicode MS, and Lucida Grande (Mac). (All of these fonts can be installed on Macintosh and Linux as well as Windows machines.)
For more information, see the following excellent sites on Greek Unicode fonts:
Typing Unicode Greek can be as straightforward as typing Greek using an old-fashioned font; see our guidelines on Greek Keyboards (Unicode)