When I was a classical greek student we used to use an online resource called perseus. I can't remember the URL but it has perseus in it at some point. As far as I can remember it wasn't easily copiable because it will only give you a few chapters at a time and so copying can be laborious. And the text used transliterations and not greek fonts if I remember rightly but once you've got the text conversion to unicode should be straighforward enough as long as the transliteration is uniform.
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